Modified optimal auxiliary functions method for approximate-analytical solutions in fractional order nonlinear Foam Drainage equations

• Published in: Partial differential equations in applied mathematics : a spin-off of Applied Mathematics Letters Vol. 10; p. 100700
• Main Authors: Ismael, Mimoon, Hat, Saba, Alabdali, Osama, Lone, Showkat Ahmad, Ali, Ali Hasan
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.06.2024; Elsevier
• Subjects: Approximation; Caputo operator; Foam Drainage equation; Fractional equations; Optimal auxiliary functions method; 65R10; Approximation; Fractional equations; 44A10; Foam Drainage equation; Optimal auxiliary functions method; 35R11; Caputo operator
• ISSN: 2666-8181; 2666-8181
• DOI: 10.1016/j.padiff.2024.100700

The study aims to obtain new approximate analytical solutions for the fractional order nonlinear Foam Drainage equation through a novel modification of the well-known Optimal Auxiliary Functions Method (OAFM). This method systematically constructs auxiliary functions, and by optimizing their parameters, it provides approximate solutions closely mirroring the original behavior of the problem. Numerical simulations, presented in tabular form, demonstrate the effectiveness of the proposed approach. Graphical representations of the solutions are utilized to further validate the applicability and accuracy of the suggested technique. Additionally, the results affirm that the modified OAFM stands out as one of the most effective tools for addressing nonlinear problems in the field of science and technology, thereby contributing valuable addition to the field.