Natural and Homotopy Techniques for Solving Fractional Differential Equations

Abstract

This research employs the natural transformation approach combined with the homotopy (N) technique, a novel and compelling hybrid method that effectively merges the homotopy approach with natural transformation (N), using a streamlined iterative procedure that minimizes computational demands. This method yields fast, convergent, and sequential solutions. The reliability of the approach is confirmed by its application to two case studies of ST-TE within the context of the Atangana-Baleanu derivative, which involves the definition of non-singular kernel functions. The study further includes thorough comparisons between approximate and exact solutions, drawing from the relevant literature to assess the method’s accuracy and effectiveness. Graphical representations highlight the influence of incorrect temporal and spatial parameters on the solution’s behavior. The findings suggest that this method is straightforward to implement and well-suited for investigating complex physical models governed by nonlinear partial differential equations with fractional time components.