New approach for the chaotic dynamical systems involving Caputo-Prabhakar fractional derivative using Adams-Bashforth scheme

Abstract

The main aim of the current paper is to propose a new numerical scheme based on the Adams-Bashforth method for solving two component time fractional differential equations involving the Caputo-Prabhakar fractional derivative of order μ. The existence and uniqueness of the solutions based on the Adams-Bashforth method reported for two component differential equations are discussed. Also, in this paper stability and convergence are demonstrated. Moreover, two numerical example are demonstrated in order to show the validity and reliability of the proposed methods.

Keywords:

• Nonlinear fractional differential equations
• Adams-Bashforth method
• Caputo-Prabhakar fractional derivative
• nonlinear chaotic dynamical systems

2010 Mathematics Subject Classifications:

• 65L05
• 65M06
• 35D05
• 65P20
• 65P40

Disclosure statement

The authors declare that they have no competing interests.