Simulating the behavior of the population dynamics using the non-local fractional Chaffee-Infante equation

Abstract

In recent years, there has been growing interest in fractional differential equations, which extend the concept of ordinary differential equations by including fractional-order derivatives. The fractional Chaffee–Infante ([Formula: see text]) equation, a nonlinear partial differential equation that describes physical systems with fractional-order dynamics, has received particular attention. Previous studies have explored analytical solutions for this equation using the method of solitary wave solutions, which seeks traveling wave solutions that are localized in space and time. To construct these solutions, the extended Khater II ([Formula: see text]) method was used in conjunction with the properties of the truncated Mittag-Leffler ([Formula: see text]) function. The resulting soliton wave solutions demonstrate how solitary waves propagate through the system and can be used to investigate the system’s response to different stimuli. The accuracy of the solutions is verified using the variational iteration [Formula: see text] technique. This study demonstrates the effectiveness of analytical and numerical methods for finding accurate solitary wave solutions to the [Formula: see text] equation, and how these methods can be used to gain insights into the behavior of physical systems with fractional-order dynamics.