A new decomposition transform method for solving nonlinear fractional logistic differential equation

In this paper, we focus on solving nonlinear fractional logistic differential equation within the Caputo-Fabrizio fractional derivative operator. First, we present a new numerical scheme called new decomposition transform method (NDTM) for solving general nonlinear fractional differential equations. The proposed scheme is obtained by combining the Jafari transform method and a new decomposition method. Furthermore, we establish the uniqueness theorem of the solution using Banach's fixed point theorem. Finally, after the convergence analysis of the NDTM, we provide two numerical examples of nonlinear fractional logistic differential equations involving the Caputo-Fabrizio fractional derivative operator to validate the results. The obtained results have shown that the new method for analytical solutions is simple to implement and very effective for analyzing the complex fractional problems that arise in related fields of science and engineering.

Automated summary

This paper presents a new numerical scheme, called New Decomposition Transform Method (NDTM), for solving nonlinear fractional differential equations. The uniqueness theorem of the solution is established using Banach's fixed point theorem. The convergence analysis and numerical examples demonstrate the effectiveness of the proposed method in analyzing complex fractional problems in various fields of science and engineering.