Variable-order (VO) fractional differential equations (FDEs) with a time (t), space (x) or other
variables dependent order have been successfully applied to investigate time and/or space …

Variable-order fractional operators were conceived and mathematically formalized only in
recent years. The possibility of formulating evolutionary governing equations has led to the …

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This paper presents the fractional formulation and numerical solution of a non-linear
fractional diffusion equation with advection and reaction terms. The fractional derivative …

In this study, we examine adapting and using the Sumudu decomposition method (SDM) as
a way to find approximate solutions to two-dimensional fractional partial differential …

A Numerical solution of the Caputo-time and Riesz-space fractional reaction–diffusion
model is considered in this paper. Based on finite difference schemes, we formulate both …

Herein, a pure shifted Jacobi–Galerkin (SJG) method is offered for handling linear two-
dimensional space-time diffusion and telegraph equations but by considering their …

This paper is primarily concern with the formulation and analysis of a reliable numerical
method based on the novel alternating direction implicit finite difference scheme for the …

This paper proposes two numerical approaches for solving the coupled nonlinear time-
fractional Burgers' equations with initial or boundary conditions on the interval 0, L 0,L. The …

This work reports a collocation algorithm for the numerical solution of a Volterra–Fredholm
integral equation (V-FIE), using shifted Chebyshev collocation (SCC) method. Some …