Innovative approaches to fractional modeling: Aboodh transform for the Keller-Segel equation

This study focuses on developing efficient numerical techniques for solving the fractional Keller-Segel (KS) model, which is critical in explaining chemotaxis events. Within the Caputo operator framework, the study applied two unique methodologies: The Aboodh residual power series method (ARPSM) and the Aboodh transform iteration method (ATIM). These approaches were used to find precise solutions to the fractional KS equation, resulting in a better understanding of chemotactic behavior in biological systems. The comparative examination of the ARPSM and ATIM revealed their distinct strengths and applications in solving complicated fractional models. The work advances numerical approaches for fractional differential equations and improves our understanding of chemotaxis dynamics using a precise modeling approach.