New Optimum solutions of The Time-Fractional Fitzhugh-Nagumo Equations

Abstract

The purpose and objective of the present work are to show the reliability and effectiveness of the newly developed semi-numerical method, i-e, the Optimal Auxiliary Function method OAFM, by solving the fractional problems of Fitzhugh-Nagumo. We have developed OAFM mathematical formulations for nonlinear partial differential equations PDEs. The implementation of the OAFM achieves a fast serial convergence solution. The analysis shows that the proposed method has a simplified implementation and needless computational work, is extremely accurate, and converges rapidly. Tables were constructed to compare the numerical results with the problems' exact solutions to see the errors.