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 …

In this manuscript, we report a new operational technique for approximating the numerical
solution of fractional optimal control (FOC) problems. The operational matrix of the Caputo …

In the present study, we introduce two new operational matrices of fractional Legendre
function vectors in the sense of generalized Caputo-type fractional derivative and …

In this manuscript, a numerical method based on the conjunction of Paraskevopoulos's
algorithm and operational matrices is developed to solve numerically the multi-order linear …

In this study, the numerically stable operational matrices are proposed to approximate the
Caputo fractional-order derivatives by introducing an algorithm. The proposed operational …

In this paper, a computational approach based on the operational matrices in conjunction
with orthogonal shifted Legendre polynomials (OSLPs) is designed to solve numerically the …

Due to the increasing application of fractional calculus in engineering and biomedical
processes, we analyze a new method for the numerical simulation of a large class of …

In this paper, we consider the discrete Hahn polynomials {H_n\} H n and investigate their
application for numerical solutions of the time fractional variable order mobile–immobile …

HAMMAD KHALIL1, KAMAL SHAH2, RAHMAT ALI KHAN2 Abstract. In this paper, we study
some properties of shifted Legendre Polynomials. Based on these polynomials, we develop …

In this paper, we produce numerical solution for a coupled system of partial differential
equations of fractional order (PDEFO) by the help of Bernstein polynomials. This method …