Application of q-Homotopy analysis method via fractional complex transformation for time fractional coupled Jaulent-Miodek equation

Abstract

In this paper, the approximate solution of time fractional coupled Jaulent-Miodek equation has been found using q-Homotopy Analysis Method (q-HAM) with the help of Fractional Complex Transformation (FCT). Fractional derivative are described in the Caputo sense. Results obtained by (q-HAM) are compared with two dimensional Hermite Wavelet method. Results of the proposed method admit a remarkable accuracy over two dimensional Hermite Wavelet method. The accuracy of (q-HAM) increases as we increase the value of n as shown in the paper. All calculation are presented with the use of Mathematica. For n = 1 (q-HAM)
reduces to Homotopy Analysis Method (HAM).