A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations. - Ali H. Bhrawy; Mahmoud A. Zaky (J. Comput. Phys., 2015)

A space-time Legendre spectral tau method for the two-sided space-time Caputo fractional diffusion-wave equation. - Ali H. Bhrawy; Mahmoud A. Zaky; Robert A. Van Gorder (Numer. Algorithms, 2016)

Highly accurate numerical schemes for multi-dimensional space variable-order fractional Schrödinger equations. - Ali H. Bhrawy; Mahmoud A. Zaky (Comput. Math. Appl., 2017)

On the formulation and numerical simulation of distributed-order fractional optimal control problems. - Mahmoud A. Zaky; J. A. Tenreiro Machado (Commun. Nonlinear Sci. Numer. Simul., 2017)

Numerical Solution of the Two-Sided Space-Time Fractional Telegraph Equation Via Chebyshev Tau Approximation. - Ali H. Bhrawy; Mahmoud A. Zaky; José António Tenreiro Machado (J. Optim. Theory Appl., 2017)

An improved tau method for the multi-dimensional fractional Rayleigh-Stokes problem for a heated generalized second grade fluid. - Mahmoud A. Zaky (Comput. Math. Appl., 2018)

New Recursive Approximations for variable-order fractional operators with Applications. - Mahmoud A. Zaky; Eid H. Doha; Taha M. Taha; Dumitru Baleanu (Math. Model. Anal., 2018)

Shifted fractional Jacobi spectral algorithm for solving distributed order time-fractional reaction-diffusion equations. - Mohamed A. Abdelkawy; António M. Lopes 001; Mahmoud A. Zaky (Comput. Appl. Math., 2019)

On the rate of convergence of spectral collocation methods for nonlinear multi-order fractional initial value problems. - Mahmoud A. Zaky; Ibrahem G. Ameen (Comput. Appl. Math., 2019)

Recovery of high order accuracy in Jacobi spectral collocation methods for fractional terminal value problems with non-smooth solutions. - Mahmoud A. Zaky (J. Comput. Appl. Math., 2019)

Multi-dimensional spectral tau methods for distributed-order fractional diffusion equations. - Mahmoud A. Zaky; J. Tenreiro Machado (Comput. Math. Appl., 2020)

High-order continuous Galerkin methods for multi-dimensional advection-reaction-diffusion problems. - Ramy M. Hafez; Mahmoud A. Zaky (Eng. Comput., 2020)

Semi-implicit Galerkin-Legendre Spectral Schemes for Nonlinear Time-Space Fractional Diffusion-Reaction Equations with Smooth and Nonsmooth Solutions. - Mahmoud A. Zaky; Ahmed S. Hendy; Jorge Eduardo Macías-Díaz (J. Sci. Comput., 2020)

A priori error estimates of a Jacobi spectral method for nonlinear systems of fractional boundary value problems and related Volterra-Fredholm integral equations with smooth solutions. - Mahmoud A. Zaky; Ibrahem G. Ameen (Numer. Algorithms, 2020)

Computational aspects of fractional Romanovski-Bessel functions. - Howayda Abo-Gabal; Mahmoud A. Zaky; Ahmed S. Hendy; Eid H. Doha (Comput. Appl. Math., 2021)

Numerical analysis of multi-term time-fractional nonlinear subdiffusion equations with time delay: What could possibly go wrong? - Mahmoud A. Zaky; Ahmed S. Hendy; Anatoly A. Alikhanov; Vladimir G. Pimenov (Commun. Nonlinear Sci. Numer. Simul., 2021)

A novel Jacob spectral method for multi-dimensional weakly singular nonlinear Volterra integral equations with nonsmooth solutions. - Mahmoud A. Zaky; Ibrahem G. Ameen (Eng. Comput., 2021)

Convergence analysis of an L1-continuous Galerkin method for nonlinear time-space fractional Schrödinger equations. - Mahmoud A. Zaky; Ahmed S. Hendy (Int. J. Comput. Math., 2021)

Singularity preserving spectral collocation method for nonlinear systems of fractional differential equations with the right-sided Caputo fractional derivative. - Ibrahem G. Ameen; Mahmoud A. Zaky; Eid H. Doha (J. Comput. Appl. Math., 2021)

A novel spectral Galerkin/Petrov-Galerkin algorithm for the multi-dimensional space-time fractional advection-diffusion-reaction equations with nonsmooth solutions. - Ramy M. Hafez; Mahmoud A. Zaky; Ahmed S. Hendy (Math. Comput. Simul., 2021)

Long time behavior of Robin boundary sub-diffusion equation with fractional partial derivatives of Caputo type in differential and difference settings. - Ahmed S. Hendy; Mahmoud A. Zaky; Mostafa Abbaszadeh (Math. Comput. Simul., 2021)

On the existence and uniqueness of solutions to a nonlinear variable order time-fractional reaction-diffusion equation with delay. - Karel Van Bockstal; Mahmoud A. Zaky; Ahmed S. Hendy (Commun. Nonlinear Sci. Numer. Simul., 2022)

A priori estimates to solutions of the time-fractional convection-diffusion-reaction equation coupled with the Darcy system. - Ahmed S. Hendy; Mahmoud A. Zaky (Commun. Nonlinear Sci. Numer. Simul., 2022)

A two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with weakly singular kernel. - Hao Chen; Mahmoud A. Zaky; Ahmed S. Hendy; Wenlin Qiu (CoRR, 2022)

Graded mesh discretization for coupled system of nonlinear multi-term time-space fractional diffusion equations. - Ahmed S. Hendy; Mahmoud A. Zaky (Eng. Comput., 2022)

On the dissipativity of some Caputo time-fractional subdiffusion models in multiple dimensions: Theoretical and numerical investigations. - Ahmed S. Hendy; Mahmoud A. Zaky; Jorge Eduardo Macías-Díaz (J. Comput. Appl. Math., 2022)

Discrete fractional stochastic Grönwall inequalities arising in the numerical analysis of multi-term fractional order stochastic differential equations. - Ahmed S. Hendy; Mahmoud A. Zaky; Durvudkhan Suragan (Math. Comput. Simul., 2022)

An easy to implement linearized numerical scheme for fractional reaction-diffusion equations with a prehistorical nonlinear source function. - Abdelrahim K. Omran; Mahmoud A. Zaky; Ahmed S. Hendy; Vladimir G. Pimenov (Math. Comput. Simul., 2022)

A note on a class of Caputo fractional differential equations with respect to another function. - Mahmoud A. Zaky; Ahmed S. Hendy; Durvudkhan Suragan (Math. Comput. Simul., 2022)

Computational and theoretical aspects of Romanovski-Bessel polynomials and their applications in spectral approximations. - Mahmoud A. Zaky; Howayda Abo-Gabal; Ramy M. Hafez; Eid H. Doha (Numer. Algorithms, 2022)

On the Rothe-Galerkin spectral discretisation for a class of variable fractional-order nonlinear wave equations. - Karel Van Bockstal; Mahmoud A. Zaky; Ahmed S. Hendy (CoRR, 2023)

Optimal error analysis of space-time second-order difference scheme for semi-linear non-local Sobolev-type equations with weakly singular kernel. - Yang Cao; Mahmoud A. Zaky; Ahmed S. Hendy; Wenlin Qiu (J. Comput. Appl. Math., 2023)

An L1 type difference/Galerkin spectral scheme for variable-order time-fractional nonlinear diffusion-reaction equations with fixed delay. - Mahmoud A. Zaky; Karel Van Bockstal; T. R. Taha; Durvudkhan Suragan; Ahmed S. Hendy (J. Comput. Appl. Math., 2023)

A re-scaling spectral collocation method for the nonlinear fractional pantograph delay differential equations with non-smooth solutions. - N. A. Elkot; Eid H. Doha; Ibrahem G. Ameen; Ahmed S. Hendy; Mahmoud A. Zaky (Commun. Nonlinear Sci. Numer. Simul., 2023)

Nonuniform difference schemes for multi-term and distributed-order fractional parabolic equations with fractional Laplacian. - Mojtaba Fardi; Mahmoud A. Zaky; Ahmed S. Hendy (Math. Comput. Simul., 2023)

Alternating direction multiplier method to estimate an unknown source term in the time-fractional diffusion equation. - Abdessamad Oulmelk; Lekbir Afraites; Aissam Hadri; Mahmoud A. Zaky; Ahmed S. Hendy (Comput. Math. Appl., 2024)

A robust alternating direction method of multipliers numerical scheme for solving geometric inverse problems in a shape optimization setting. - Julius Fergy T. Rabago; Aissam Hadri; Lekbir Afraites; Ahmed S. Hendy; Mahmoud A. Zaky (Comput. Math. Appl., 2024)

A second-order finite difference scheme for nonlinear tempered fractional integrodifferential equations in three dimensions. - R. Wang; L. Qiao; Mahmoud A. Zaky; Ahmed S. Hendy (Numer. Algorithms, 2024)

Supervised learning and meshless methods for two-dimensional fractional PDEs on irregular domains. - Mostafa Abbaszadeh; Mahmoud A. Zaky; Ahmed S. Hendy; Mehdi Dehghan 002 (Math. Comput. Simul., 2024)

Temporal Second-Order Fast Finite Difference/Compact Difference Schemes for Time-Fractional Generalized Burgers' Equations. - Xiangyi Peng; Wenlin Qiu; Ahmed S. Hendy; Mahmoud A. Zaky (J. Sci. Comput., 2024)

Chebyshev polynomial derivative-based spectral tau approach for solving high-order differential equations. - Marwa Gamal; Mahmoud A. Zaky; Mamdouh El-Kady; Mohamed Abdelhakem (Comput. Appl. Math., 2024)

An easy-to-implement recursive fractional spectral-Galerkin method for multi-term weakly singular Volterra integral equations with non-smooth solutions. - Younes Talaei; Mahmoud A. Zaky; Ahmed S. Hendy (Numer. Algorithms, 2024)

Virtual element approximation and BDF2 time-discrete scheme for a partial integro-differential equation with a singular Abel's kernel. - Mostafa Abbaszadeh; Mahmoud A. Zaky; Mehdi Dehghan 002 (Appl. Math. Comput., 2025)

Nonsmooth optimization method for determining nonsmooth potential parameter in nonlinear subdiffusion equation. - Abdessamad Oulmelk; Lekbir Afraites; Aissam Hadri; Mahmoud A. Zaky; Ahmed S. Hendy; Xiangcheng Zheng; Hong Wang (Commun. Nonlinear Sci. Numer. Simul., 2025)

Learning primal-dual approach for space-dependent diffusion coefficient identification in fractional diffusion equations. - Mohammed Srati; Abdessamad Oulmelk; Lekbir Afraites; Aissam Hadri; Mahmoud A. Zaky; Ahmed S. Hendy (J. Comput. Phys., 2025)

On a computational paradigm for a class of fractional order direct and inverse problems in terms of physics-informed neural networks with the attention mechanism. - Mohammed Srati; Abdessamad Oulmelk; Lekbir Afraites; Aissam Hadri; Mahmoud A. Zaky; Ahmed S. Hendy (J. Comput. Sci., 2025)

Spatial two-grid compact difference method for nonlinear Volterra integro-differential equation with Abel kernel. - Hao Chen; Mahmoud A. Zaky; Xiangcheng Zheng; Ahmed S. Hendy; Wenlin Qiu (Numer. Algorithms, 2025)

Mapped Legendre-spectral method for high-dimensional multi-term time-fractional diffusion-wave equation with non-smooth solution. - H. Moussa; M. A. Saker; Mahmoud A. Zaky; M. Babatin; Samer S. Ezz-Eldien (Comput. Appl. Math., 2025)