Numerical solutions for nonlinear multi-term fractional differential equations via Dickson operational matrix

Abstract

The purpose of this paper is to present a novel numerical technique for solving a class of nonlinear multi-term fractional differential equations. The proposed method mainly relies on using the Dickson polynomial to derive the Dickson operational matrix of fractional derivative, which is then used to solve the given problem. The fundamental significance of this strategy is that it converts the fractional problem into a system of nonlinear equations that can be numerically solved. In addition, the error bound of the suggested method is deduced. Numerical experiments are presented to verify and confirm the accuracy of the suggested technique for dealing with such problems.

Keywords:

• Operational matrix
• Dickson polynomials
• nonlinear multi-term fractional differential equations

2010 AMS SUBJECT CLASSIFICATIONS:

• 26A33
• 65L70
• 34K28
• 65M70

Disclosure statement

No potential conflict of interest was reported by the author.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.