In this review paper, we are mainly concerned with the numerical methods for solving
fractional equations, which are divided into the fractional differential equations (FDEs), time …

We develop efficient algorithms based on the Legendre-tau approximation for one-and two-
dimensional fractional Rayleigh–Stokes problems for a generalized second-grade fluid. The …

We introduce a class of orthogonal functions associated with integral and fractional
differential equations with a logarithmic kernel. These functions are generated by applying a …

This paper presents a computational method for the approximate solution of arbitrary-order
non-linear fractional Riccati differential equations with variable coefficients. Proposed …

An open problem in the numerical analysis of spectral methods for fractional differential
equations is how to maintain the high-order accuracy for non-smooth solutions. The limited …

In this paper, we consider a new fractional function based on Legendre and Laguerre
polynomials for solving a class of linear and nonlinear time-space fractional partial …

In this paper, we develop a range of efficient and fast fractional difference schemes for the
approximation of Caputo time-fractional subdiffusion-reaction equations. The classical time …

The primary point of this manuscript is to dissect and execute a new modified Galerkin
algorithm based on the shifted Jacobi polynomials for solving fractional differential …

In this article, we have explored the numerical solution of fourth order fractional boundary
value problems, involving product terms, by means of quintic spline collocation method. The …

This paper provides the Riesz potential and fractional Laplacian (− Δ) s, s∈ R of the famous
radial kernels, including the Gaussian, multiquadric, Sobolev spline, and mainly focuses on …