Approximate Analytical Solution for Non-Linear Fitzhugh–Nagumo Equation of Time Fractional Order Through Fractional Reduced Differential Transform Method

The fractional reduced differential transform method (FRDTM) is frequently used to solve linear and non-linear fractional differential equations of ordinary and partial type is revisited in the present work. The FRDTM is implemented to solve the non-linear Fitzhugh–Nagumo equation of time fractional order. The present article is more concerned to demonstrate the accuracy and rapid convergence of the FRDTM to get true solutions of non-linear partial differential equations of fractional order. The present algorithm is observed the faster convergence in comparison with the prevailed classical methods i.e. Homotopy perturbation method (HPM) and Adomian decomposition method (ADM). The 2-terms approximated result through FRDTM is compared with the exact solutions. The accuracy of the proposed method is demonstrated over HPM and ADM methods through comparison tables and error graphs at different values of space and time. The effect of different fractional derivatives to the solution behavior of the the non-linear Fitzhugh–Nagumo equation of time fractional order is shown through the graphs at x= 1. The present work gives wider description of FRDTM and provides approximate results in terms of convergent series. The FRDTM is quite powerful tool in terms of efficiency and effectiveness. The small size of computation contrary to the HPM and ADM methods is its main advantage. The novelty of the present work lies in the study of comparison analysis of FRDTM with prevailed methods HPM and ADM.