Picard and Adomian solutions of nonlinear fractional differential equations system containing Atangana – Baleanu derivative

Abstract

Abstract In this paper, we apply two methods for solving nonlinear system of fractional differential equations (FDEs); these two methods are Picard and Adomian decomposition methods (ADM). The type of fractional derivative in this system will be the Atangana–Baleanu derivative. The existence and uniqueness of the solution will be proved. In addition, the convergence of ADM series solution and the maximum expected error will be discussed. Some numerical examples will be solved by using these two method and a comparison between their solutions will be done. There exist an important application to these types of systems, this application is the fractional-order rabies model and it will be solved here. From the obtained results, it is noticed that the obtained results from using these two methods are coincide with each other, and also these results are coincide with the obtained results from the classical fractional derivatives such as Caputo sense.

Keywords

• Fractional differential equations
• Atangana – Baleanu derivative
• Picard and Adomian decomposition methods
• Existence and uniqueness
• Error analysis
• Fractional-order rabies model