Fractional-order view analysis of Fisher’s and foam drainage equations within Aboodh transform

Abstract

PurposeThe purpose of this study is to solve two unique but difficult partial differential equations: the foam drainage equation and the nonlinear time-fractional fisher’s equation. Through our methods, we aim to provide accurate solutions and gain a deeper understanding of the intricate behaviors exhibited by these systems.Design/methodology/approachIn this study, we use a dual technique that combines the Aboodh residual power series method and the Aboodh transform iteration method, both of which are combined with the Caputo operator.FindingsWe develop exact and efficient solutions by merging these unique methodologies. Our results, presented through illustrative figures and data, demonstrate the efficacy and versatility of the Aboodh methods in tackling such complex mathematical models.Originality/valueOwing to their fractional derivatives and nonlinear behavior, these equations are crucial in modeling complex processes and confront analytical complications in various scientific and engineering contexts.

An innovative approach to approximating solutions of fractional partial differential equations

“…F-DEs (fractional differential equations) have become highly significant in numerous engineering and scientific fields owing to their ability to efficiently represent intricate occurrences that involve memory effects and non-local behavior. F-DEs have been successfully applied in areas such as physics, chemistry, biology, finance, and control theory [1,4,18,23,24,26,[28][29][30]32]. One important application of F-DEs is in modeling anomalous diffusion processes.…”