Advancing Solutions for Fractional Differential Equations: Integrating the Sawi Transform with Iterative Methods

Abstract

This paper presents a powerful approach to solving fractional differential equations by combining the Sawi transform with iterative methods, particularly the Sawi iterative method. We begin by reviewing the fundamental properties and theoretical aspects of the Sawi transform, demonstrating its effectiveness in simplifying and solving fractional differential equations. The integration of the Sawi transform with the iterative method is applied to solve fractional delay differential equations, showcasing both analytical and approximate solutions through detailed examples and case studies. Our findings highlight that this combined approach not only streamlines the solution process but also significantly enhances the accuracy and applicability of solutions across a diverse range of differential equations. This study lays a robust foundation for further research and practical applications, offering valuable insights and tools for advancing scientific and engineering fields.