Document Type : Research Paper
Author
Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, Ferhat Abbas Sétif University 1, 19000 Sétif, Algeria.
Abstract
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
Main Subjects
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