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A Legendre collocation method for distributed-order fractional optimal control problems

Nonlinear dynamics, 2018-03, Vol.91 (4), p.2667-2681

Zaky, Mahmoud A.

2018

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An improved tau method for the multi-dimensional fractional Rayleigh–Stokes problem for a heated generalized second grade fluid

Computers & mathematics with applications (1987), 2018-04, Vol.75 (7), p.2243-2258

Zaky, Mahmoud A.

2018

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A Legendre spectral quadrature tau method for the multi-term time-fractional diffusion equations

Computation and applied mathematics, 2018-07, Vol.37 (3), p.3525-3538

Zaky, Mahmoud A.

2018

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Graded mesh discretization for coupled system of nonlinear multi-term time-space fractional diffusion equations

Engineering with computers, 2022-04, Vol.38 (2), p.1351-1363

2022

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Multi-dimensional spectral tau methods for distributed-order fractional diffusion equations

Computers & mathematics with applications (1987), 2020-01, Vol.79 (2), p.476-488

2020

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Combined Galerkin spectral/finite difference method over graded meshes for the generalized nonlinear fractional Schrödinger equation

Nonlinear dynamics, 2021-02, Vol.103 (3), p.2493-2507

2021

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Semi-implicit Galerkin–Legendre Spectral Schemes for Nonlinear Time-Space Fractional Diffusion–Reaction Equations with Smooth and Nonsmooth Solutions

Journal of scientific computing, 2020, Vol.82 (1), p.13, Article 13

2020

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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

Numerical algorithms, 2020-05, Vol.84 (1), p.63-89

2020

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Convergence analysis of an L1-continuous Galerkin method for nonlinear time-space fractional Schrödinger equations

International journal of computer mathematics, 2021-07, Vol.98 (7), p.1420-1437

2021

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Convergence analysis of a Legendre spectral collocation method for nonlinear Fredholm integral equations in multidimensions

Mathematical methods in the applied sciences, 2024-09, Vol.47 (13), p.10717-10730

2024

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A novel Jacob spectral method for multi-dimensional weakly singular nonlinear Volterra integral equations with nonsmooth solutions

Engineering with computers, 2021-10, Vol.37 (4), p.2623-2631

2021

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Temporal Second-Order Fast Finite Difference/Compact Difference Schemes for Time-Fractional Generalized Burgers’ Equations

Journal of scientific computing, 2024-05, Vol.99 (2), p.52, Article 52

2024

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Theoretical and numerical aspects for the longtime behavior of nonlinear delay time Caputo fractional reaction–diffusion equations

Nonlinear dynamics, 2023-02, Vol.111 (4), p.3525-3537

2023

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A priori estimates to solutions of the time-fractional convection–diffusion–reaction equation coupled with the Darcy system

Communications in nonlinear science & numerical simulation, 2022-06, Vol.109, p.106288, Article 106288

2022

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An easy-to-implement recursive fractional spectral-Galerkin method for multi-term weakly singular Volterra integral equations with non-smooth solutions

Numerical algorithms, 2024-11, Vol.97 (3), p.1089-1117

2024

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High-order continuous Galerkin methods for multi-dimensional advection–reaction–diffusion problems

Engineering with computers, 2020-10, Vol.36 (4), p.1813-1829

2020

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A research note on the nonstandard finite difference method for solving variable-order fractional optimal control problems

Journal of vibration and control, 2018-06, Vol.24 (11), p.2109-2111

Zaky, Mahmoud A

2018

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Numerical analysis of multi-term time-fractional nonlinear subdiffusion equations with time delay: What could possibly go wrong?

Communications in nonlinear science & numerical simulation, 2021-05, Vol.96, p.105672, Article 105672

2021

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Well-posedness analysis and pseudo-Galerkin approximations using Tau Legendre algorithm for fractional systems of delay differential models regarding Hilfer (α,β)-framework set

PloS one, 2024-06, Vol.19 (6), p.e0305259

2024

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The impact of memory effect on space fractional strong quantum couplers with tunable decay behavior and its numerical simulation

Scientific reports, 2021-05, Vol.11 (1), p.10275-10275, Article 10275

2021

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A two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with weakly singular kernel

Calcolo, 2023-03, Vol.60 (1), Article 13

2023

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Global Existence for Two Singular One-Dimensional Nonlinear Viscoelastic Equations with respect to Distributed Delay Term

Journal of function spaces, 2021, Vol.2021, p.1-18

2021

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Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation

PloS one, 2023-05, Vol.18 (5), p.e0283746-e0283746

2023

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Crank-Nicolson/finite element approximation for the Schrödinger equation in the de Sitter spacetime

Physica scripta, 2021-12, Vol.96 (12), p.124010

2021

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High‐order finite difference/spectral‐Galerkin approximations for the nonlinear time–space fractional Ginzburg–Landau equation

Numerical methods for partial differential equations, 2023-11, Vol.39 (6), p.4549-4574

2023

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A Legendre collocation method for distributed-order fractional optimal control problems

An improved tau method for the multi-dimensional fractional Rayleigh–Stokes problem for a heated generalized second grade fluid

A Legendre spectral quadrature tau method for the multi-term time-fractional diffusion equations

Graded mesh discretization for coupled system of nonlinear multi-term time-space fractional diffusion equations

Multi-dimensional spectral tau methods for distributed-order fractional diffusion equations

Combined Galerkin spectral/finite difference method over graded meshes for the generalized nonlinear fractional Schrödinger equation

Semi-implicit Galerkin–Legendre Spectral Schemes for Nonlinear Time-Space Fractional Diffusion–Reaction Equations with Smooth and Nonsmooth Solutions

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

Convergence analysis of an L1-continuous Galerkin method for nonlinear time-space fractional Schrödinger equations

Convergence analysis of a Legendre spectral collocation method for nonlinear Fredholm integral equations in multidimensions

A novel Jacob spectral method for multi-dimensional weakly singular nonlinear Volterra integral equations with nonsmooth solutions

Temporal Second-Order Fast Finite Difference/Compact Difference Schemes for Time-Fractional Generalized Burgers’ Equations

Theoretical and numerical aspects for the longtime behavior of nonlinear delay time Caputo fractional reaction–diffusion equations

A priori estimates to solutions of the time-fractional convection–diffusion–reaction equation coupled with the Darcy system

An easy-to-implement recursive fractional spectral-Galerkin method for multi-term weakly singular Volterra integral equations with non-smooth solutions

High-order continuous Galerkin methods for multi-dimensional advection–reaction–diffusion problems

A research note on the nonstandard finite difference method for solving variable-order fractional optimal control problems

Numerical analysis of multi-term time-fractional nonlinear subdiffusion equations with time delay: What could possibly go wrong?

Well-posedness analysis and pseudo-Galerkin approximations using Tau Legendre algorithm for fractional systems of delay differential models regarding Hilfer (α,β)-framework set

The impact of memory effect on space fractional strong quantum couplers with tunable decay behavior and its numerical simulation

A two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with weakly singular kernel

Global Existence for Two Singular One-Dimensional Nonlinear Viscoelastic Equations with respect to Distributed Delay Term

Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation

Crank-Nicolson/finite element approximation for the Schrödinger equation in the de Sitter spacetime

High‐order finite difference/spectral‐Galerkin approximations for the nonlinear time–space fractional Ginzburg–Landau equation

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