An efficient technique to solve coupled–time fractional Boussinesq–Burger equation using fractional decomposition method

Abstract

For this work, a novel numerical approach is proposed to obtain solution for the class of coupled time-fractional Boussinesq–Burger equations which is a nonlinear system. This system under consideration is endowed with Caputo time-fractional derivative. By means of the natural decomposition approach, approximate solutions of the proposed nonlinear fractional system are obtained where the exact solutions are presented in the classical case of fractional order at γ = 1 . Some numerical examples are given to support the theoretical framework and to point out the role and the effectiveness of the intended method. Our results clearly show the approximate analytical solutions eventually will converge quickly to the already known exact solutions. AMS Classification: 35A22, 35C05, 35C10, 35R11, 44A30.