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

M. Basim; N. Senu; A. Ahmadian; Z. B. Ibrahim; S. Salahshour

doi:10.46481/jnsps.2023.1221

Authors

M. Basim
maisbasim777@yahoo.com
Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM, Serdang, Malaysia
N. Senu Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM, Serdang, Malaysia | Department of Mathematics and statistics Universiti Putra Malaysia, 43400 UPM, Serdang, Malaysia
A. Ahmadian Decision Lab, Mediterranea University of Reggio Calabria, Reggio Calabria, Italy
Z. B. Ibrahim Department of Mathematics and statistics Universiti Putra Malaysia, 43400 UPM, Serdang, Malaysia
S. Salahshour Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey

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.

Dimensions

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