Numerical Solution of Fractional Burger-KdV Equation Using Double Natural-Aboodh Transform Method

Abstract

n this research, the fractional Burger-KdV partial differential equation is studied; two integral transform; the Natural Transform and Aboodh Transform were used to develop a new Double integral transform called Double Natural-Aboodh transform; the Double Natural-Aboodh Transform, combined with the Adomian Decomposition method, was employed to obtain the series-form solution when fractional order equal one and numerical solution of fractional Burger-KdV equation. The Caputo fractional operator was adopted; existence and uniqueness of the method were investigated in Caputo fractional derivative. The solution was found to be unique and convergent. Two example problems were provided to illustrate the efficiency, simplicity and accuracy of the developed method when compared with the existence literatures.