Profile

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Mohammad Hossein Heydari

Associate Professor of applied mathematics

Academic Appointments

Associate Professor of Applied and Computational Mathematics, Shiraz University of Technology, Shiraz, Iran, February 2022 until now.
Assistant Professor of Applied and Computational Mathematics, Shiraz University of Technology, Shiraz, Iran, February 2018 to February 2022.

Honors & Awards

The World's Top 1 Percent Scientists in Mathematics, for the Year 2023.
The World's Top 1 Percent Scientists in Mathematics, for the Year 2022.
The World's Top 1 Percent Scientists in Mathematics, for the Year 2021.
The World's Top 2 Percent Scientists in Mathematics, for the Year 2020.
Distinguished Researcher at Fars Province/Iran-2023.
Distinguished Researcher/Shiraz University of Technology/Iran-2022.
Distinguished Researcher/Shiraz University of Technology/Iran-2021.
Distinguished Researcher/Shiraz University of Technology/Iran-2020.
Distinguished Researcher at Fars Province/Iran-2019.
Distinguished Researcher/Shiraz University of Technology/Iran-2018.
Distinguished Researcher Student/Yazd University/Iran-2011, 2012, 2014.

Contact

Email: heydari@sutech.ac.ir

Professional Education

Ph. D.: Applied Mathematics, Yazd University, Iran, 2010-2014, (Dissertation title: Numerical solutions of differential equations of fractional order by wavlet bases).
M. Sc.: Applied Mathematics (Numerical Analysis), Yazd University, Iran, 2008–2010, (Thesis title: Numerical solutions of functional equations by iterative methods).
B. Sc.: Applied Mathematics, Razi University of Kermanshah, Iran, 2002-2006.

Courses

Teaching Experiences

Postgraduate: Spectral Methods, Numerical Methods for Integral Equations, Numerical Methods for Fractional Differential Equations, Advanced Optimal Control.
Graduate: Calculus I, II, Ordinary Differential Equations, Basic Numerical Analysis, Numerical Linear Algebra, Numerical Computations, Preliminary Stochastic Calculus, Mathematical software.

SUTech advisees

Supervisor of PhD students

Fatemeh Hosseininia, PhD candidate in Applied Mathematics, Numerical Analysis, Yazd University, Iran, (joint with Prof. Farid Mohammad Maalek Ghaini).
Fatemeh Alsadat Aghayi Maybodi, PhD candidate in Applied Mathematics, Numerical Analysis, Yazd University, Iran, (joint with Prof. Farid Mohammad Maalek Ghaini).

Advisor of PhD and MSc students

Fatemeh Soltani Sarvestani, PhD candidate in Pure Mathematics, Harmonic Analysis, Ferdowsi University of Mashhad, Iran, (joint with Prof. Asadollah Niknam).
Khadejeh Mousavi, PhD candidate in Pure Mathematics, Analysis, Shahid Bahonar University of Kerman, Iran, (joint with Prof. Ataollah Askari Hemmat).
Parisa Mohammadi, MSc student in Applied Mathematics, Mathematical Finance, Yazd University, Iran, (joint with Prof. Mohammad Reza Hooshmandasl).

Current Research

Spectral and Meshless Methods in Mechanical Engineering Problems.
Fractional Modeling of Applied Problems and Their Numerical Solutions.
Spectral Methods for Solving Constant- and Variable-Order Fractional Optimal Control Problems.
Numerical Methods for Statistical Problems.

All Publications

Book Chapters

M. H. Heydari, A. Shakiba, Z. Avazzadeh, C. Cattani, Second Kind Chebyshev Wavelets for Solving the Variable-Order Space-Time Fractional Telegraph Equation, Special Functions and Analysis of Differential Equations, (2020) 63-85.

Publications

M. H. Heydari, Sh. Zhagharian, M. Razzaghi, Jacobi polynomials for the numerical solution of multi-dimensional stochastic multi-order time fractional diffusion-wave equations, Computers and Mathematics with Applications, 152, 91–101, 2023.
M. H. Heydari, M. Razzaghi, Sh. Karami, Orthonormal Chelyshkov polynomials for multi-term time fractional two-dimensional telegraph type equations, Results in Physics, 55, 107161, 2023.
M. H. Heydari, Sh. Zhagharian, Genocchi polynomials for variable-order time fractional Fornberg–Whitham type equations, Partial Differential Equations in Applied Mathematics, 8, 100554, 2023.
M. Hosseininia, M. H. Heydari, M. Razzaghi,A hybrid spectral approach based on 2D cardinal and classical second kind Chebyshev polynomials for time fractional 3D Sobolev equation, Mathematical Methods in the Applied Sciences, 46(18), 18768–18788, 2023.
O. Bavi, M. Hosseininia, M. H. Heydari, A mathematical model for precise predicting microbial propagation based on solving variable-order fractional diffusion equation, Mathematical Methods in the Applied Sciences, 46(16), 17313–17327, 2023.
P. Rahimkhani, M. H. Heydari, Fractional shifted Morgan–Voyce neural networks for solving fractal-fractional pantograph differential equations, Chaos, Solitons and Fractals, 175, 114070, 2023.
J. Nazari, M. H. Heydari, M. Hosseininia, Romanovski–Jacobi polynomials for the numerical solution of multi-dimensional multi-order time fractional telegraph equations, Results in Physics, 53, 106937, 2023.
H. Azin, M. H. Heydari, O. Baghani, F. Mohammadi, Fractional Vieta-Fibonacci wavelets: Application for systems of fractionaldelay differential equations, Physica Scripta, 98(9), 095242, 2023.
F. Afiatdoust, M. H. Heydari, M. M. Hosseini, A block-by-block strategy for fractional systems of nonlinear weakly singular integro-differential equations, Computational and Applied Mathematics, 42, 252, 2023.
M. H. Heydari, A computational approach for a system of coupled distributed-order fractional Klein-Gordon-Schrodinger equations, Results in Physics, 51, 106750, 2023.
H. Heydari, Sh. Zhagharian, A hybrid approach for piecewise fractional reaction-diffusion equations, Results in Physics, 51, 106651, 2023.
M. H. Heydari, M. Haji Shaabani, Z. Rasti, Orthonormal discrete Legendre polynomials for nonlinear reaction-diffusion equations with ABC fractional derivative and non-local boundary conditions, Mathematical Methods in the Applied Science, 46(12), 13423-13435, 2023.
M. H.‎ Heydari, M.‎ Razzaghi, A hybrid method based on the Chebyshev cardinal functions/wavelets for time fractional coupled Klein-Gordon-Schrodinger equations, Journal of Computational and Applied Mathematics, 427, 115142, 2023.
M. H. Heydari, M. Razzaghi, D. Baleanu, Orthonormal piecewise Vieta-Lucas functions for the numerical solution of the one- and two-dimensional piecewise fractional Galilei invariant advection-diffusion equations, Journal of Advanced Research, 49, 175-190, 2023.
M. H. Heydari, M. Hosseininia, An efficient Jacobi spectral method for variable-order time fractional 2D Wu-Zhang system, Computers and Mathematics with Applications, 140, 89-106, 2023.
M. H. Heydari, A cardinal approach for two-dimensional modified anomalous space–time fractional sub-diffusion equation, Results in Physics, 49, 106545, 2023.
M. H. Heydari, M. Razzaghi, Piecewise fractional Chebyshev cardinal functions: Application for time fractional Ginzburg–Landau equation with a non-smooth solution, Chaos, Solitons and Fractals, 171, 113445, 2023
M. H. Heydari, A. Atangana, A numerical method for nonlinear fractional reaction–advection–diffusion equation with piecewise fractional derivative, Mathematical Science, 17(2), 169-181, 2023.
O. Bavi, M. Hosseininia, M. Hajishamsaei, M. H. Heydari, Glioblastoma multiforme growth prediction using a Proliferation-Invasion model based on nonlinear time-fractional 2D diffusion equation, Chaos, Solitons and Fractals, 170,113393, 2023.
A. Habibirad, E. Hesameddini, H. Azin, M. H. Heydari, The direct meshless local Petrov–Galerkin technique with its error estimate for distributed-order time fractional Cable equation, Engineering Analysis with Boundary Elements, 150, 342-352, 2023.
M.H. Heydari, S. Rashid, Yu-Ming Chu, Chelyshkov polynomials method for distributed-order time fractional nonlinear diffusion-wave equations, Results in Physics, 47, 106344, 2023.
M. H. Heydari, M. Hosseininia, D, Baleanu, A computational approach based on the fractional Euler functions and Chebyshev cardinal functions for distributed-order time fractional 2D diffusion equation, Alexandria Engineering Journal, 67, 643-653, 2023.
M. H. Heydari, M. Razzaghi, D. Baleanu, Numerical solution of distributed-order time fractional Klein–Gordon–Zakharov system, Journal of Computational Science, 67, 101961, 2023.
M. H. Heydari, M. Razzaghi, Z. Avazzadeh, Orthonormal piecewise Bernoulli functions: Application for optimal control problems generated using fractional integro-differential equations, Journal of Vibration and Control, 29 (5-6), 1164-1175, 2023.
M. H.‎ Heydari, M.‎ Razzaghi, Highly accurate solutions for space–time fractional Schrödinger equations with non-smooth continuous solution using the hybrid clique functions, Mathematical Sciences, 17(1), 31-42, 2023.
M. H. Heydari, S. Rashid, F. Jarad, A numerical method for distributed-order time fractional 2D Sobolev equation, 45, 106211, 2023.
Afiatdoost, M. H. Heydari, M. M. Hosseini, A block-by-block method for nonlinear variable-order fractional quadratic integral equations, Computational and Applied Mathematics, 42, 38, 2023.
Sh. Zhagharian, M. H. Heydari, M. Razzaghi, A numerical method for two-dimensional distributed-order fractional nonlinear Sobolev equation, Journal of Applied Analysis and Computation, 13 (5), 2630-2645, 2023.
F. Afiatdoust, M. H. Heydari, M. M. Hosseini, A block-by-block approach for nonlinear fractional integro-differential equations, International Journal of Computer Mathematics, 2023, 100(11), pp. 2140–2155.
M. H. Heydari, M. Razzaghi, Sh. Zhagharian, Numerical solution of distributed-order fractional 2D optimal control problems using the Bernstein polynomials, International Journal of Systems Science, 54(10), 2253-2267, 2023.
M. H.‎ Heydari, M. Hosseininia, D. Baleanu, An efficient method for 3D Helmholtz equation with complex solution, AIMS Mathematics 8(6), 14792-14819.
‎ M. H.‎ Heydari, M.‎ Razzaghi, C. Cattani, Fractional Chebyshev cardinal wavelets: application for fractional quadratic integro-differential equations, International Journal of Computer Mathematics, 100 (3), 479-496, 2023.
M. H.‎ Heydari, M.‎ Razzaghi, D. Baleanu, A numerical method based on the piecewise Jacobi functions for distributed-order fractional Schrödinger equation, Communications in Nonlinear Science and Numerical Simulations, 116, 106873, 2023.
Karami, A. Fakharzadeh Jahromi, M. H. Heydari, A computational method based on the generalized Lucas polynomials for fractional optimal control problems, Advances in Continous and Discrete Models, 2022, 64, 2022.
M. H. Heydari, M. Hosseininia, M. Razzaghi, Meshless local Petrov-Galerkin method for 2D fractional Fokker-Planck equation involved with the ABC fractional derivative, Computer and Mathematics with Applications, 125, 176—192, 2022.
M. H. Heydari, O. Bavi, An efficient wavelet method for nonlinear problems arising in heat transfer, Engineering with Computers, 38, 2867-2878, 2022.
Habibirad, R. Roohi, E. Hesamddini, M. H. Heydari, A reliable algorithm to determine the pollution transport within underground reservoirs: implementation of an efficient collocation meshless method based on the moving Kriging interpolation, Engineering with Computers, 38, 2781-2795, 2022.
‎ M. H.‎ Heydari, M.‎ Razzaghi, J. Rouzegar, Chebyshev cardinal polynomials for delay distributed-order fractional fourth-order sub-diffusion equation, Chaos, Solitons and Fractals, 162, 112495, 2022.
Hosseininia, M. H. Heydari, Z. Avazzadeh, A hybrid wavelet-meshless method for variable-order fractional regularized long-wave equation, Engineering Analysis with Boundary Elements, 138, 108-117, 2022.
Hosseininia, M. H. Heydari, Z. Avazzadeh, A hybrid wavelet-meshless method for variable-order fractional regularized long-wave equation, Engineering Analysis with Boundary Elements, 138, 108-117, 2022.
M. H. Heydari, O. Bavi, An optimization method based on the Legendre wavelets for 3D rotating, squeezing and stretching magnetohydrodymanic flow in a channel with porous wall, Engineering with Computers, 38, 2583-2592, 2022.
M. H. Heydari, M. Razzaghi, Z. Avazzadeh, Orthonormal Bernoulli polynomials for space–time fractal-fractional modified Benjamin–Bona–Mahony type equations, Engineering with Computers, 38(4), 3483-3496, 2022.
Roohi, and M. Hosseininia, M. H. Heydari, A wavelet approach for the variable-order fractional model of ultra-short pulsed laser therapy, Engineering with Computers, 38, 2229-2244, 2022.
M. H. Heydari, Z. Avazzadeh, A hybrid method for variable-order fractional 2D optimal control problems on an unbounded domain, Engineering with Computers, 38(4), 3237-3249, 2022.
‎ M. H.‎ Heydari, M.‎ Razzaghi, Third-kind Chebyshev cardinal functions for variable-order time fractional RLW-Burgers equation, Mathematical Methods in the Applied Sciences, Sciences, 45(10), 5670-5681, 2022. ‎
M. H. Heydari, Z. Avazzadeh, C. Cattani, Orthonormal shifted discrete Hahn polynomials for a new category of nonlinear variable-order fractional 2D optimal control problems, Asian Journal of Control, 24(4), 986-1997, 2022.
M. Hosseininia,M.H. Heydari, Z. Avazzadeh, A hybrid approach established upon the Müntz-Legender functions and 2D Müntz-Legender wavelets for fractional Sobolev equation, Mathematical Methods in the Applied Sciences, 45(9), 5304-5320, 2022.
M. H. Heydari, Z. Avazzadeh, Jacobi–Gauss–Lobatto collocation approach for non-singular variable-order time fractional generalized Kuramoto–Sivashinsky equation, Engineering with Computers, 38, 925-937, 2022.
O. Bavi, M. Hosseininia, M. H. Heydari, N. Bavi, SARS-CoV-2 rate of spread in and across tissue, groundwater and soil: A meshless algorithm for the fractional diffusion equation, Engineering Analysis with Boundary Elements, 138, 108-117, 2022.
J. Ansari, A. R. Abbasi, M. H. Heydari, Z. Avazzaded, Simultaneous design of fuzzy PSS and fuzzy STATCOM controllers for power system stability enhancement, Alexandria Engineering Journal, 41(4) (2022), 2841-2850 .
M. H. Heydari, Z. Avazzadeh, C. Cattani, Numerical solution of variable-order space-time fractional KdV-Burgers-Kuramoto equation by using discrete Legendre polynomials, Engineering with Computers, 38, 859-869, 2022.
M. H. Heydari, Z. Avazzadeh, Chebyshev-Gauss-Lobatto collocation method for variable-order time fractional generalized Hirota-Satsuma coupled KdV system, Engineering with Computers, 38(2), 1835-1844, 2022.
M. H. Heydari, M. Hosseininia, A new variable-order fractional derivative with non-singular Mittag-Leffler kernel: application to variable-order fractional version of the 2D Richard equation, Engineering with Computers, 38(2), 1759-1770, 2022.
O. Bavi, M. Ozmaeian, M. H. Heydari, Editorial: Biomechanics and Mechanobiology, Frontiers in Mechanical Engineering, 8, 863175, 2022.
M. H. Heydari, M. Razzaghi, Jacobi spectral method for variable-order fractional Benney–Lin equation arising in falling film problems, Journal of Computational and Applied Mathematics, 402 (2022), 113813.
M. Hosseininia, M. H. Heydari, Z. Avazzadeh, Orthonormal shifted discrete Legendre polynomials for the variable-order fractional extended Fisher–Kolmogorov equation, Chaos, Solitons and Fractals, 155 (2022), 111729.
M. H. Heydari, Z. Avazzadeh, Numerical study of non-singular variable-order time fractional coupled Burgers' equations by using the Hahn polynomials, Engineering with Computers, 38(1), 101-110, 2022.
H. Azin, M. H. Heydari, F. Mohammadi, Vieta–Fibonacci wavelets: Application in solving fractional pantograph equations, Mathematical Methods in the Applied Sciences, 45(1) (2022), 411-422.
M. H. Heydari, R. Tavakoli, M. Razzaghi, Application of the extended Chebyshev cardinal wavelets in solving fractional optimal control problems with ABC fractional derivative, International Journal of Systems Science, 53(12), 2694-2708.
H. Heydari, M. Razzaghi, Extended Chebyshev cardinal wavelets for nonlinear fractional delay optimal control problems, International Journal of Systems Science, 35(5), 1048-1067, 2022.
M. H. Heydari, M. Razzaghi, A new class of orthonormal basis functions: application for fractional optimal control problems, International Journal of Systems Science, 53(2), (2022), 240-252.
M. H. Heydari, A. Atangana, An accurate approach based on the orthonormal shifted discrete Legendre polynomials for variable-order fractional Sobolev equation, Advances in Difference Equations, 2021, 272, 2021.
M. H. Heydari, Z. Avazzadeh, A. Atangana, Shifted Jacobi polynomials for nonlinear singular variable-order time fractional Emden–Fowler equation generated by derivative with non-singular kernel, Advances in Difference Equations, 2021 (2021), 188.
M. H. Heydari, M. Razzaghi, A numerical approach for a class of nonlinear optimal control problems with piecewise fractional derivative, Chaos, Solitons and Fractals, 152 (2021), 111465.
M. H. Heydari, O. Bavi, An optimal variational iteration method for investigating the physical behavior of quasi-steady squeezing flow confined between parallel rigid walls, Physica Scripta, 96(11) (2021), 114012.
M. H. Heydari, Z. Avazzadeh, A direct computational method for nonlinear variable-order fractional delay optimal control problems, Asian Journal of Control, 23(6)(2021), 2709-2718.
M. H. Heydari, Z. Avazzadeh, New formulation of the orthonormal Bernoulli polynomials for solving the variable-order time fractional coupled Boussinesq–Burger’s equations, Engineering with Computers, 37(4) (2021), 3509-35-17.
M. Hosseininia, M. H. Heydari, Z. Avazzadeh, Numerical study of the variable-order fractional version of the nonlinear fourth-order 2D diffusion-wave equation via 2D Chebyshev wavelets, Engineering with Computers, 37(4) (2021), 3319-3328.
M. H. Heydari, M. Razzaghi, Piecewise Chebyshev cardinal functions: Application for constrained fractional optimal control problems, Chaos, Solitons and Fractals, 150 (2021), 111118.
M. H. Heydari, M. Razzaghi, Z. Avazzadeh, Numerical investigation of variable-order fractional Benjamin–Bona–Mahony–Burgers equation using a pseudo-spectral method, Mathematical Methods in the Applied Sciences, 44(11) (2021), 8669-8683.
M. H. Heydari, Z. Avazzadeh, M. Razzaghi, Vieta-Lucas polynomials for the coupled nonlinear variable-order fractional Ginzburg-Landau equations, Applied Numerical Mathematics, 165 (2021), 442-458.
M. Hosseininia, M. H. Heydai, C. Cattani, A wavelet method for nonlinear variable-order time fractional 2D Schrödinger equation, Discrete & Continuous Dynamical Systems - S, 14(7) (2021), 2273-2295.
M. Hosseininia, M. H. Heydari, Z. Avazzadeh, An efficient wavelet-based approximation method for the coupled nonlinear fractal–fractional 2D Schrödinger equations, Engineering with Computers, 37(3) (2021), 2129-2144.
M. Hosseininia, M. H. Heydari, Z. Avazzadeh, F. M. Maalek Ghaini, A hybrid method based on the orthogonal Bernoulli polynomials and radial basis functions for variable order fractional reaction-advection-diffusion equation, Engineering Analysis with Boundary Elements, 127 (2021), 18-28.
M. Hosseininia, M. H. Heydari, F. M. Maalek Ghaini, Z. Avazzadeh, A meshless technique based on the moving least squares shape functions for nonlinear fractal-fractional advection-diffusion equation, Engineering Analysis with Boundary Elements, 127 (2021), 8-17.
M. H. Heydari, Z. Avazzadeh, Fibonacci polynomials for the numerical solution of variable-order space-time fractional Burgers-Huxley equation, Mathematical Methods in the Applied Sciences, 44(8) (2021), 6774-6786.
M. H. Heydari, Z. Avazzadeh, A. Atangana, Shifted Vieta-Fibonacci polynomials for the fractal-fractional fifth-order KdV equation, Mathematical Methods in the Applied Sciences, 44(8) (2021), 6716-6730.
M. Hosseininia, M. H. Heydari, F. M. Maalek Ghaini, A numerical method for variable-order fractional version of the coupled 2D Burgers equations by the 2D Chelyshkov polynomials, Mathematical Methods in the Applied Sciences, 44(8) (2021), 6482-6499.
R. Roohi, M. H. Heydai, Z. Avazzadeh, Optimal control of hyperthermia thermal damage based on tumor configuration, Results in Physics, 23 (2021), 103992.
M. H. Heydari, A. Atangana, Z. Avazzadeh, Chebyshev polynomials for the numerical solution of fractal–fractional model of nonlinear Ginzburg–Landau equation, Engineering with Computers, 37(2) (2021), 1377-1388.
A. Habibirad, S. Hesameddini, M. H. Heydai, R. Roohi, An efficient meshless method based on the moving Kriging interpolation for two-dimensional variable-order time fractional mobile/immobile advection-diffusion model, Mathematical Methods in the Applied Sciences, 44(4) (2021), 3182-3194.
M. H. Heydari, Z. Avazzadeh, Orthonormal Bernstein polynomials for solving nonlinear variable-order time fractional fourth-order diffusion-wave equation with nonsingular fractional derivative, Mathematical Methods in the Applied Sciences, 44(4) (2021), 3098-3110.
M. H. Heydari, A, Atangana, Numerical solution of nonlinear fractal-fractional optimal control problems by Legendre polynomials, Mathematical Methods in the Applied Sciences, 44(4) (2021), 2952-2963.
M. H. Heydari, Z. Avazzadeh, A. Atangana, Orthonormal shifted discrete Legendre polynomials for solving a coupled system of nonlinear variable-order time fractional reaction-advection-diffusion equation, Applied Numerical Mathematics, 161 (2021), 425-436.
M. H. Heydari, M. Razzaghi, Z. Avazzadeh, Orthonormal shifted discrete Chebyshev polynomials: Application for a fractal-fractional version of the coupled Schrödinger-Boussinesq system, Chaos, Solitons and Fractals, 143 (2021), 110570.
M. R. Mahmoudi, M. H. Heydari, S. N. Qasem, A. Mosavi, S. Band, Principal component analysis to study the relations between the spread rates of COVID-19 in high risks countries, Alexandria Engineering Journal, 60(1) (2021) 457-464.
M. H. Heydari, Z. Avazzadeh, C. Cattani, Discrete Chebyshev polynomials for nonsingular variable-order fractional KdV Burgers' equation, Mathematical Methods in the Applied Sciences, 44(2) (2021), 2158-2170.
M. Hosseininia, M. H. Heydari, M. R. Hooshmandasl, F. M. Maalek Ghaini, Z. Avazzadeh, A numerical method based on the Chebyshev cardinal functions for variable-order fractional version of the fourth-order 2D Kuramoto-Sivashinsky equation, Mathematical Methods in the Applied Sciences, 44(2) (2021), 1831-1842.
M. H. Heydari, M. Hosseininia, J. Rouzegar, C. Cattani, A meshless method to solve nonlinear variable-order time fractional 2D reaction–diffusion equation involving Mittag-Leffler kernel, Engineering with Computers, 37 (1) (2021), 731-743.
R. Roohi, M.‎ H.‎ Heydari, O. Bavi, H. Emdad, Chebyshev polynomials for generalized Couette flow of fractional Jeffrey nanofluid subjected to several thermochemical effects, Engineering with Computers, 37 (1) (2021), 579-595 .
F. S. Aghaei Maybodi, M.‎ H.‎ Heydari, F. M. Maalek Ghaini, Ghaussian-Radial basis functions for solving fractional partial integro-differential equations, Journal of mathematical Extension, 15(2) (2021) 1-21.
J. Rouzegar, M. Vazirzadeh, M. H. Heydari, A fractional viscoelastic model for vibrational analysis of thin plate excited by supports movement, Mechanics Research Communications, 110 (2020), 103618.
Y. Yang, M. H. Heydari, Z. Avazzadeh, A. Atangana, Chebyshev wavelets operational matrices for solving nonlinear variable-order fractional integral equations, Advances in Difference Equations, https://doi.org/10.1186/s13662-020-03047-4, (2020) .
H. Azin, F. Mohammadi, M. H. Heydari, A hybrid method for solving time fractional advection–diffusion equation on unbounded space domain, Advances in Difference Equations 2020 (2020).
A. Shadloo-Jahromi, O. Bavi, M. H. Heydari, M. Kharati-Koopaee, Z. Avazzadeh, Dynamics of respiratory droplets carrying SARS-CoV-2 virus in closed atmosphere, Results in Physics, 19 (2020), 103482.
M. H. Heydari, Z. Avazzadeh, C. Cattani, Taylor's series expansion method for nonlinear variable-order fractional 2D optimal control problems, Alexandria Engineering Journal, 59(6) (2020), 4737-4743.
M. H. Heydari, Z. Avazzadeh, Y. Yang, Numerical treatment of the space-time fractal-fractional model of nonlinear advection-diffusion-reaction equation through the Bernstein polynomials, Fractal, 28(8) (2020) 2040001 (14 pages).
M. Hosseininia, M. H. Heydari, Z. Avazzadeh, The numerical treatment of nonlinear fractal-fractional 2D Emden-Fowler equation utilizing 2D Chelyshkov polynomials, Fractal, 28 (8) (2020) 2040042 (12 pages).
M. H. Heydari, M. Hosseininia, A. Atangana, Z. Avazzadeh, A meshless approach for solving nonlinear variable-order time fractional 2D Ginzburg-Landau equation, Engineering Analysis with Boundary Elements, 120 (2020) 166-179.
M. Maleki, M. R Mahmoudi, M. H. Heydari, K. H. Pho, Modeling and forecasting the spread and death rate of coronavirus (COVID-19) in the world using time series models, Chaos, Solitons & Fractals, 140 (2020) 110151.
B. K. Mousavi, M. H. Heydari, Wilson wavelets method for solving nonlinear fractional Fredholm–Hammerstein integro-differential equations, International Journal of Computer Mathematics, 97(11) (2020), 2165-2177.
D. Gharian, F. M. Maalek Ghaini, M. H. Heydari, Z Avazzadeh, A meshless solution for the variable-order time fractional nonlinear Klein–Gordon equation, International Journal of Applied and Computational Mathematics, 6 (5) (2020) 1-16.
M. R. Mahmoudi, M. H. Heydari, K. H. Pho, Fuzzy clustering to classify several regression models with fractional Brownian motion errors, Alexandria Engineering Journal, 59 (4) (2020), 2811-2818.
Z. Avazzadeh, M. H. Heydari, M. R. Mahmoudi, An approximate approach for the generalized variable-order fractional pantograph equation, Alexandria Engineering Journal, 59(4) (2020) 2347-2354.
M. H. Heydari, A. Atangana, Z. Avazzadeh, Y. Yang, Numerical treatment of the strongly coupled nonlinear fractal-fractional Schrödinger equations through the shifted Chebyshev cardinal functions, Alexandria Engineering Journal, 59(4) (2020) 2037-2052.
M. H. Heydari, A computational method for a class of systems of nonlinear variable-order fractional quadratic integral equations, Applied Numerical Mathematics, 153 (2020) 164-178.
K. H. Pho, M. H Heydari, B. A. Tuan, M. R. Mahmoudi, Numerical study of nonlinear 2D optimal control problems with multi-term variable-order fractional derivatives in the Atangana-Baleanu-Caputo sense, Chaos, Solitons & Fractals 134 (2020) 109695.
M. H. Heydari, M. R. Mahmoudi, Z. Avazzadeh, D. Baleanu, Chebyshev cardinal functions for a new class of nonlinear optimal control problems with dynamical systems of weakly singular variable-order fractional integral equations, Journal of Vibration and Control, 26 (9-10) (2020) 713-723.
M. H. Heydari, Z. Avazzadeh, A computational method for solving two-dimensional nonlinear variable-order fractional optimal control problems, Asian Journal of Control, 22 (3) (2020) 1112-1126.
M. H. Heydari, Numerical solution of nonlinear 2D optimal control problems generated by Atangana-Riemann-Liouville fractal-fractional derivative, Applied Numerical Mathematics, 150 (2020) 507-518.
M. H. Heydari, A. Atangana, An optimization method based on the generalized Lucas polynomials for variable-order space-time fractional mobile-immobile advection-dispersion equation involving derivatives with non-singular kernels, Chaos, Solitons & Fractals, 132 (2020) 109588.
M. H. Heydari, Z. Avazzadeh, Y. Yang, C. Cattani, A cardinal method to solve coupled nonlinear variable-order time fractional sine-Gordon equations, A cardinal method to solve coupled nonlinear variable-order time fractional sine-Gordon equations, Computational and Applied Mathematics 39 (2) (2020).
M. H. Heydari, M. R. Hooshmandasl, C. Cattani, Wavelets method for solving nonlinear stochastic Itô-Volterra integral equations, Georgian Mathematical Journal, 27(1)(2020), 81-95.
M. H. Heydari, A. Atangana, Z. Avazzadeh, M. R. Mahmoudi, An operational matrix method for nonlinear variable-order time fractional reaction–diffusion equation involving Mittag-Leffler kernel, The European Physical Journal Plus, 135 (2) (2020) 1-19.
M. R. Mahmuodi, M. H. Heydari, Z. Avazzadeh, K. H. Pho, Goodness of fit test for almost cyclostationary processes, Digital Signal Processing, 96, (2020) 102597.
M.‎ H.‎ Heydari, Chebyshev cardinal functions for a new class of nonlinear optimal control problems generated by Atangana–Baleanu–Caputo variable-order fractional derivative, Chaos, Solitons & Fractals, 130 (2020), https://doi.org/10.1016/j.chaos. 2019.109401.
M. Hosseininia, M.‎ H.‎ Heydari, F. M. Maalek Ghaini, Z. Avazzadeh, A wavelet method to solve nonlinear variable-order time fractional 2D Klein–Gordon equation, Computer and Mathematics with Applications, 78 (12) (2019) 3713-3730.
Z. Ma, M.‎ H.‎ Heydari, Z. Avazzadeh, C. Cattani, An efficient iterative approach for three-dimensional modified anomalous fractional sub-diffusion equations on a large domain, Advances in Difference Equations, (2019) 2019: 367, https://doi.org/10.1186/s13662-019-2302-2.
M.‎ H.‎ Heydari, A. Atangana, A cardinal approach for nonlinear variable-order time fractional Schrödinger equation defined by Atangana–Baleanu–Caputo derivative, Chaos, Solitons & Fractals, 128 (2019) 339-348.
M. Hosseininia, M.‎ H.‎ Heydari, R. Roohi, Z. Avazzadeh, A computational wavelet method for variable-order fractional model of dual phase lag bioheat equation, Journal of Computational Physics, 395 (2019) 1-18.
R. Roohi, M. H. Heydari, H. G. Sun, Numerical study of unsteady natural convection of variable-order fractional Jeffrey nanofluid over an oscillating plate in a porous medium involved with magnetic, chemical and heat absorption effects using Chebyshev cardinal functions, The European Physical Journal Plus, 143 (2019) 535.
M. Hosseininia, M.‎ H.‎ Heydari, Legendre wavelets for the numerical solution of nonlinear variable-order time fractional 2D reaction-diffusion equation involving Mittag–Leffler non-singular kernel, Chaos, Solitons and Fractals, 127 (2019) 400-407.
M. Hosseininia, M.‎ H.‎ Heydari, Meshfree moving least squares method for nonlinear variable-order time fractional 2D telegraph equation involving Mittag–Leffler non-singular kernel, Chaos, Solitons and Fractals, 127 (2019) 389-399.
M.‎ H.‎ Heydari, A direct method based on the Chebyshev polynomials for a new class of nonlinear variable-order fractional 2D optimal control problems, Journal of the Franklin Institute, 356 (15) (2019) 8216-8236.
M.‎ H.‎ Heydari, Chebyshev cardinal wavelets for nonlinear variable-order fractional quadratic integral equations, Applied Numerical Mathematics, 144 (2019) 190-203.‎
Z. Avazzadeh, M.‎ H.‎ Heydari, C. Cattani, Legendre wavelets for fractional partial integro-differential viscoelastic equations with weakly singular kernels, The European Physical Journal Plus, 134 (7) (2019), 368.
M.‎ H.‎ Heydari, Z.‎ Avazzadeh, M.‎ R.‎ Mahmoudi, Chebyshev cardinal wavelets for nonlinear stochastic differential equations driven with variable-order fractional Brownian motion, Chaos, Solitons and Fractals, 124 (2019) 105-124.‎
M.‎ H.‎ Heydari, Z.‎ Avazzadeh, Y.‎ Yang, A computational method for solving variable-order fractional nonlinear diffusion-wave equation, Applied Mathematics and Computation, 352 (2019) 235-248.
Y.‎ Shekari, A.‎ Tayebi, M.‎ H.‎ Heydari, A meshfree approach for solving 2D variable-order fractional nonlinear diffusion-wave equation, Computer Methods in Applied Mechanics and Engineering, 350 (2019), 154-168.
M.‎ R.‎ Mahmoudi, M.‎ H.‎ Heydari, R.‎ Roohi, A new method to compare the spectral densities of two independent periodically correlated time series, Mathematics and Computers in Simulation,160 (2019) 103-110.
M. R. Mahmoudi, M. H. Heydari, Z. Avazzadeh, Testing the difference between spectral densities of two independent periodically correlated (cyclostationary) time series models, Communications in Statistics-Theory and Methods, 48(9) (2019) 2320-2328.
F.‎ Soltani Sarvestani, M.‎ H.‎ Heydari, A.‎ Niknam, Z.‎ Avazzadeh, A wavelet approach for the multi-term time fractional diffusion-wave equation, International Journal of Computer Mathematics, 96 (3) (2019) 640-661.
M. H. Heydari, Z. Avazzadeh, M. Farzi Haromi, A wavelet approach for solving multi-term variable-order time fractional diffusion-wave equation, Applied Mathematics and Computations, 341 (2019) 215–228.
D. Gharian, F. M. Maalek Ghaini, M. H. Heydari, A meshless method for variable-order time fractional telegraph equation, Journal of Mathematical Extension, 13(3) (2019) 35-56.
M. Hosseininia, M. H. Heydari, Z. Avazzadeh, F. M. Maalek Ghaini, Two-dimensional Legendre wavelets for solving variable-order fractional nonlinear advection-diffusion equation with variable coefficients, International Journal of Nonlinear Sciences and Numerical Simulation, 19(7-8) (2018) 793-802.
R. Roohi, M. H. Heydari, M. Aslami, M. R. Mahmoudi, A comprehensive numerical study of space-time fractional bioheat equation using fractional-order Legendre functions, The European Physical Journal Plus, 13(10) (2018) 1-15.
M. R. Mahmoudi, M. H. Heydari, Z. Avazzadeh, On the asymptotic distribution for the periodograms of almost periodically correlated (cyclostationary) processes, Digital Signal Processing, 81 (2018) 186–197.
M. H. Heydari, A new direct method based on the Chebyshev cardinal functions for variableorder fractional optimal control problems, Journal of the Franklin Institute, 355 (2018) 4970-4995.
M. H. Heydari, Z. Avazzadeh, Legendre wavelets optimization method for variable-order fractional Poisson equation, Chaos, Solitons and Fractals, 12 (2018) 180-190.
M. H. Heydari, M. R. Mahmoudi, A. Shakiba, Z. Avazzadeh, Chebyshev cardinal wavelets and their application in solving nonlinear stochastic differential equations with fractional Brownian motion, Communications in Nonlinear Science and Numerical Simulation, 64 (2018) 98-121.
M. H. Heydari, Z. Avazzadeh, A new wavelet method for variable-order fractional optimal control problems, Asian Journal of Control, 20 (5) (2018) 1-14.
M. H. Heydari, Z. Avazzadeh, An operational matrix method for solving variable-order fractional biharmonic equation, Computational and Applied Mathematics, (2018) 1-15.
M. H. Heydari, H. Laeli Dastjerdi, M. Nili Ahmadabadi, An efficient method for the numerical solution of a class of nonlinear fractional Fredholm integro-differential equations, International Journal of Nonlinear Sciences and Numerical Simulation, 19 (2018) 165–173.
A. Mardani, M. R. Hooshmandasl, M. H. Heydari, C. Cattani, A meshless method for solving time fractional advection-diffusion equation with variable coefficients, Computer and Mathematics with Applications, 75 (2018) 122-133.
M. R. Hooshmandasl, M. H. Heydari, C. Cattani, A new operational matrix of fractional order integration for the Chebyshev wavelets and its application for nonlinear fractional order Van der Pol oscillator equation, Proceeding Mathematical Sciences, 128:26 (2018) 1-26.
M. Salai Mathi Selvi, G.Hariharan, K.Kannan, M. H. Heydari, Two reliable computational methods pertaining to steady state substrate concentration of an immobilized enzyme system, Alexandria Engineering Journal, 55(4) (2018) 2377-2385.
A. Tayebi, Y. Shekari, M. H. Heydari, A meshless method for solving two-dimensional variable order time fractional advection-diffusion equation, Journal of computational physics, 340 (2017) 655-669.
A. Mardani, M. R. Hooshmandasl, M. M. Hosseini, M. H. Heydari, Moving least squares (MLS) method for the nonlinear hyperbolic telegraph equation with variable coefficients, International Journal of Computational Methods, 2 (2017) 1750026 (19 pages).
M. H. Heydari, M. R. Hooshmandasl, C. Cattani, G. Hariharan, An optimization wavelet Method for multi Variable-order fractional differential equations, Fundamenta Informaticae, 151 (2017) 255–273.
H. Hassani, M. Shafie Dahaghin, M. H. Heydari, A. Bayati Eshkaftaki, A new optimization method based on generalized polynomials for fractional differential equations, Fundamenta Informaticae, 151 (2017) 443–457.
H. Hassani, M. Sh. Dahaghin, M. H. Heydari, A new optimized method for solving variable order fractional differential equations, Journal of Mathematical Extension, 11 (2017) 85-98.
M. H. Heydari, M. R. Hooshmandasl, F. M. Maalek Ghaini, C. Cattani, Wavelets method for solving fractional optimal control problems, Applied Mathematics and Computations, 286 (2016) 139–154.
M. H. Heydari, M. R. Hooshmandasl, A. Shakiba, C. Cattani, Legendre wavelets Galerkin method for solving nonlinear stochastic integral equations, Nonlinear Dynamic, 85 (2) (2016)1185-1202.
M. H. Heydari, M. R. Hooshmandasl, F. M. Maalek Ghaini, M. Fatehi, R. Dehghan Simakani, M. H. Memarian, A new wavelet method for solving the Helmholtz equation with complexsolution, Numerical Methods for Partial Differential Equations, 32 (3) (2016) 741-756.
M. H. Heydari, M. R. Hooshmandasla, Gh. Barid Loghmania, C. Cattani, Wavelets Galerkin method for solving stochastic heat equation, International Journal of Computer Mathematics, 9 (2016) 1579-1596.
M. R. Hooshmandasl, M. H. Heydari, C. Cattani, Numerical solution of fractional sub-diffusion and time fractional diffusion-wave equations via fractional-order Legendre functions, TheEuropean Physical Journal-Plus, 2016, 131: 268.
M. H. Heydari, Wavelets Galerkin method for the fractional sub-diffusion equation, Computational and Nonlinear Dynamics, 11 (2016) 061014-7.
M. H. Heydari, M. R. Hooshmandasl, F. M. Maalek Ghaini, C. Cattani , An efficient computational method based on the hat functions for solving fractional optimal control problems, Tbilisi Mathematical Journal, 9 (1) (2016) 143-157.
M. H. Heydari, M. R. Hooshmandasl, C.Cattani, F.M.Maalek Ghaini, An efficient computational method for solving nonlinear stochastic Ito-Volterra integral equations: Application forstochastic problems in physics, Journal of Computational Physics, 283 (2015) 148–168.
M. H. Heydari, M. R. Hooshmandasl, F. M. Maalek Ghaini, C. Cattani, Wavelets method for the time fractional diffusion-wave equation, Physics Letters A, 379 (2015) 71–76.
M. H. Heydari, M. R. Hooshmandasl, F. M. Maalek Ghaini, C. Cattani, A computational method for solving stochastic Ito-Volterra integral equations based on stochastic operational matrix for generalized hat basis functions, Journal of Computational Physics, 270 (2014)402–415.
M. H. Heydari, M. R. Hooshmandasl, F. Mohammadi, C. Cattani, Wavelets method for solving systems of nonlinear singular fractional Volterra integro-differential equations, Commun Nonlinear Sci and Numer Simu., 19 (1) (2014) 1007-5704.
M. H. Heydari, M. R. Hooshmandasl, F. M. Maalek Ghaini, An efficient computational method for solving fractional biharmonic equation, Computer and Mathematics with Applications, 68(2014) 269-287.
M. H. Heydari, M. R. Hooshmandasl, F. M. Maalek Ghaini, A new approach of the Chebyshev wavelets method for partial differential equations with boundary conditions of the telegraph type, Applied Mathematical Modeling, 38 (2014) 1597–1606.
M. H. Heydari, M. R. Hooshmandasl, F. Mohammadi, Legendre wavelets method for solving fractional partial differential equations with Dirichlet boundary conditions, Applied mathematicsand computation, 234 (2014) 267–276.
M. H. Heydari, M. R. Hooshmandasl, F. Mohammadi, Two-Dimensional Legendre Wavelets for Solving Time-Fractional Telegraph Equation, Advances in Applied Mathematics and Mechanics,6(2)(2014) 247-260.
M. H. Heydari, M. R. Hooshmandasl, F. M. Maalek Ghaini, F. Feriedouni, Two-dimensional Legendre wavelets for solving fractional Poisson equation with Dirichlet boundary conditions, Engineering Analysis with Boundary Elements, 37 (2013) 1331–1338.
M. H. Heydari, M. R. Hooshmandasl, C. Cattani, M. Li, Legendre wavelets method for solving fractional population growth model in a closed system, Mathematical Problems in Engineering, Volume 2013, Article ID 161030, 8 pages.
M. H. Heydari, M. R. Hooshmandasl, F. M. Maalek Ghaini, M. Li, Chebyshev wavelets method for solution of nonlinear fractional integrodifferential equations in a large interval, Advances in Mathematical Physics, Volume 2013, Article ID 482083, 12 pages.
M. H. Heydari, M. R. Hooshmandasl, F. M. Maalek Ghaini, A good approximate solution for Lienard equation in a large interval using block pulse functions, Journal of Mathematical Extension, 7 (2012) 17-32.
B. Kh. Mousavi, A. Askari Hemmat, M. H. Heydari, Wilson wavelets for nonlinear stochastic integral equations of Hammerstein type, Wavelets and Linear Algebra, 4 (2) (2017) 33-48.
M. H. Heydari, M. R Hooshmandasl, F. Mohammadi, A. Ciancio, Solution of nonlinear singular initial value problems of generalized Lane-Emden type using block pulse functions in a largeinterval, Waves, Wavelets and Fractals, 2 (1) (2016) 7-19.
M. H. Heydari, F. M. Maalek Ghaini, Legendre wavelets method for numerical solution of time-fractional heat equation, Wavelets and Linear Algebra, 1 (2014) 13-22.
M. H. Heydari, M. R. Hooshmandasl, F. M. Maalek Ghaini, Numerical solution of the one dimensional heat equation by using Chebyshev wavelets collocation method, Journal of Applied and Computational Mathematics, 16 (2012) 1-7.
M. H. Heydari, M. M. Hosseini, M. R. Hooshmandasl, S. T. Mohyud-Din, Ghaini, Reliable approach of iterative method for nonlinear fractional differential equation, International Journalof the Physical Sciences, 6 (2011) 6917-6927.
M. M. Hosseini, M. H. Heydari, M. R. Hooshmandasl, He's Homotopy perturbation method for solving Pochhammer-Chree equations, Middle East Journal of Scientific Research, 7 (2011)943-946.
M. M. Hosseini, M. H. Heydari, A Note on Iterative Method for Solving Nonlinear Functional Equation, Journal of Advanced Research in Applied Mathematics, 1 (2009) 27-33.

Conference Papers

F. M. Maalek Ghaini, F. S. Aghaei Maybodi, M.‎ H.‎ Heydari, M. H.‎ Akrami, Numerical solving of fractional parabolic partial integro-differential equations by Gaussian radial basis function, 7th International Seminar of Numerical Analysis and its Applications, Shahid Bahonar University of Kerman, Iran, ‪(July 2018)‬.‎
F.‎ Soltani Sarvestani, M.‎ H.‎ Heydari, A.‎ Niknam, Wavelets method for nonlinear fractional partial integro-differential equations, 3th Seminar on Operator Theory and its Applications, Ferdowsi University of Mashhad, Iran, ‪(March 2017)‬.‎
F. Soltani Sarvestani, M. H. Heydari, A. Niknam, Wavelets method for solving a class of fractional partial integro-differential equations, 5th Seminar on Harmonic Analysis and Applications, Ferdowsi University of Mashhad, Iran, (January 2017).
F. Haghshenas, M. H. Heydari, M. R. Hooshmandasl, A new approach of Chebyshev wavelets collocation method for telegraph equation, 9th Seminar on Differential Equations and DynamicalSystems, Tabriz, Iran, (July 2012).
M. R. Hooshmandasl, M. H. Heydari, Solution of nonlinear multi-order fractional equations by Legendre wavelets method, 43th Annual Iranian Mathematics Conference, Tabriz, Iran, (August 2012).
M. H. Heydari, M. R. Hooshmandasl, Chebyshev wavelet operational matrix of the fractional integration for solving nonlinear multi-order fractional differential equations, 42th Annual Iranian Mathematics Conference, Rafsanjan, Iran, (September 2011).
M. H. Heydari, M. R. Hooshmandasl, M. M. Hosseini, Iterative-Laurent method for solving nonlinear fractional differential equations, 42th Annual Iranian Mathematics Conference, Rafsanjan, Iran, (September 2011 ).
M. M. Hosseini, M. H. Heydari, Iterative-Taylor method for solving system of nonlinear partial differential equations, 4th Iranian Conference of Applied Mathematics, Sistan and Balochestan, Iran, (March 2010).
M. M. Hosseini, M. H. Heydari, Numerical solution of sine-Gordon equations by Iterative-Taylor methods, 4th Iranian Conference of Applied Mathematics, Sistan and Balochestan, Iran, (March 2010).