# Solving fractional variable-order differential equations of the non-singular derivative using Jacobi operational matrix

## Keywords:

FDEs; Non-singular derivative; Variable order; Operational matrix.## Abstract

This research derives the shifted Jacobi operational matrix (JOM) with respect to fractional derivatives, implemented with the spectral tau method for the numerical solution of the Atangana-Baleanu Caputo (ABC) derivative. The major aspect of this method is that it considerably simplifies problems by reducing them to ones that can be solved by solving a set of algebraic equations. The main advantage of this method is its high robustness and accuracy gained by a small number of Jacobi functions. The suggested approaches are applied in solving non-linear and linear ABC problems according to initial conditions, and the efficiency and applicability of the proposed method are proved by several test examples. A lot of focus is placed on contrasting the numerical outcomes discovered by the new algorithm together with those discovered by previously well-known methods.

## Published

## How to Cite

*Journal of the Nigerian Society of Physical Sciences*,

*5*(2), 1221. https://doi.org/10.46481/jnsps.2023.1221

## Issue

## Section

Copyright (c) 2023 M. Basim, N. Senu, A. Ahmadian, Z. B. Ibrahim

This work is licensed under a Creative Commons Attribution 4.0 International License.

## How to Cite

*Journal of the Nigerian Society of Physical Sciences*,

*5*(2), 1221. https://doi.org/10.46481/jnsps.2023.1221