Adaptation of the Optimal Auxiliary Function Method for Solving Highly Non Linear System of Fractional Order Partial Differential Equations (Global Journal of Sciences, 2025)
This research work represents the analysis of time-fractional system of highly non linear partial differential equation by applying the Optimal Auxiliary Function method (OAFM) while taking fractional derivative in Caputo sense. The OAFM does not require any polynomials like ADM method and small parameters like Perturbation method. The OAFM contains auxiliary constant which control the convergence of approximate solution in excellent way. Mathematica 13 is utilized to illustrate 2-dimensional curves and three-dimensional graphs and find numerical values that are displayed in a table. Furthermore, the OAFM and the exact solutions are compared. The numerical analysis reveals that the method is both valid and efficient as well as the suitability of the error bound. The results further demonstrate that the OAFM method is an effective approach for solving nonlinear physical models.
Keywords: Caputo derivative; System of Fractional; Order Partial Differential; Equations; Optimal Auxiliary; Functions Method