Existence, Uniqueness and Convergence Solution of Nonlinear Caputo-Fabrizio Fractional Biological Population Model

This paper studies a fractional biological population model involving the Caputo-Fabrizio fractional derivative. We establish the existence and uniqueness of the solution using Banach's fixed point theorem. Furthermore, we propose a new numerical algorithm called \mathbb{J}-decomposition method (\mathbb{J}-DM) which is a combined form of the \mathbb{J}-transform method and a new decomposition method to solve the proposed model. After the convergence analysis of the \mathbb{J}-DM, we provide three numerical examples to illustrate the results obtained. The numerical examples show that this method is easy to use and can give accurate results.

Keywords:

Fractional biological population model , Caputo-Fabrizio fractional derivative , Banach space , J-transform , Decomposition method