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

Authors

  • M. Basim
    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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Published

2023-05-05

How to Cite

Solving fractional variable-order differential equations of the non-singular derivative using Jacobi operational matrix. (2023). Journal of the Nigerian Society of Physical Sciences, 5(2), 1221. https://doi.org/10.46481/jnsps.2023.1221

Issue

Volume 5, Issue 2, May 2023

Section

Original Research
Copyright & Licensing

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

Creative Commons License

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

How to Cite

Solving fractional variable-order differential equations of the non-singular derivative using Jacobi operational matrix. (2023). Journal of the Nigerian Society of Physical Sciences, 5(2), 1221. https://doi.org/10.46481/jnsps.2023.1221

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