Laplace Residual Power Series Solutions of the Fractional Modified KdV System with Physical Applications

In this paper, we construct approximate series solutions for the general fractional modified KdV system (MKdV-S) in Caputo’s sense using a new analytical technique called the Laplace residual power series method (L-RPSM). The main advantage of our new technique is that it provides better accuracy and faster convergence of series solutions compared to other methods, and it requires a few computations for finding the coefficients of terms of series solutions by using only the concept of limit at infinity without involving discretization, perturbation, or any other physical restriction conditions. In addition, two attractive physical applications coming from fractional MKdV-S are given and examined by making a comparison between our obtained results for solving the fractional MKdV-S by L-RPSM, and other well-known methods such as the variational iteration method (VIM), Adomian decomposition method (ADM), q-homotopy analysis transform method (q-HATM), and homotopy analysis method (HAM). Finally, several attractive numerical tests and graphical results are also given and discussed.