Solitary wave solutions and traveling wave solutions for systems of time-fractional nonlinear wave equations via an analytical approach

Abstract

This paper introduces a new approximate-analytical approach for solving systems of Fractional Nonlinear Partial Differential Equations (FNPDEs). However, the main advantage of this new approximate-analytical approach is to obtain the analytical solution for general systems of FNPDEs in forms of convergent series with easily computable components using Caputo fractional partial derivative. Moreover, the convergence theorem and error analysis of the proposed method are also shown. Solitary wave solutions and traveling wave solutions for the system of fractional dispersive wave equations and the system of fractional long water wave equations are successfully obtained. The numerical solutions are also obtained in forms of tables and graphs to confirm the accuracy and efficiency of the suggested method.