Approximate Analytical Solutions to the One-Dimensional Fisher Equation Via Conformable Fractional Reduced Differential Transform Method

Abstract

In many branches of science, such as population dynamics, ecology, and epidemic modeling, the one-dimensional Fisher equation is very important. In this study, we recommend using the conformable fractional reduced differential transform method (CFRDTM) to get approximate analytical solutions for the one-dimensional Fisher equation. A strong mathematical method known as the CFRDTM combines the benefits of the conformable fractional calculus and the reduced differential transform method (RDTM). The conformable fractional calculus offers a more accurate depiction of the underlying physical events while the RDTM makes it possible to convert the original differential equation into a collection of algebraic equations. By employing the CFRDTM, we derive an approximate analytical solution for the one-dimensional Fisher equation. The convergence of the approximate solutions are analyzed and compared with existing approximation methods that exists in the literature. Furthermore, the proposed CFRDTM is validated through two test examples. Overall, this research contributes to the development of efficient and accurate analytical methods for obtaining approximate solutions to the one-dimensional Fisher equation and related nonlinear partial differential equations