Open Access

ARTICLE

On Nonlinear Conformable Fractional Order Dynamical System via Differential Transform Method

by Kamal Shah^1,2, Thabet Abdeljawad^3,4,*, Fahd Jarad⁵, Qasem Al-Mdallal⁶

1 Department of Mathematics and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia
2 Department of Mathematics, University of Malakand, Chakdara Dir (L), Khyber Pakhtunkhwa, 18000, Pakistan
3 Department of Mathematics and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia
4 Department of Medical Research, China Medical University, Taichung, 40402, Taiwan
5 Department of Mathematics, Faculty of Arts and Sciences, Çankaya University, Ankara, 06790, Turkey
6 Department of Mathematical Sciences, UAE University, Al-Ain, 15551, United Arab Emirates

* Corresponding Author: Thabet Abdeljawad. Email:

(This article belongs to the Special Issue: Advanced Numerical Methods for Fractional Differential Equations)

Computer Modeling in Engineering & Sciences 2023, 136(2), 1457-1472. https://doi.org/10.32604/cmes.2023.021523

Received 18 January 2022; Accepted 26 September 2022; Issue published 06 February 2023

Abstract

This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system. For the proposed study, we consider the model under the conformable fractional order derivative (CFOD). We investigate the mentioned dynamical system for the existence and uniqueness of at least one solution. Indeed, Schauder and Banach fixed point theorems are utilized to prove our claim. Further, an algorithm for the approximate analytical solution to the proposed problem has been established. In this regard, the conformable fractional differential transform (CFDT) technique is used to compute the required results in the form of a series. Using Matlab-16, we simulate the series solution to illustrate our results graphically. Finally, a comparison of our solution to that obtained for the Caputo fractional order derivative via the perturbation method is given.

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Keywords

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