Approximate Analytical Solutions of Two-Dimensional Time Fractional KleinGordon Equation

Abstract

This study presents a fractional reduced differential transform method (FRDTM) to find approximate analytical solutions of nonlinear time  fractional two dimensional Klein Gordon equation. The fractional derivative used in this study is in the Caputo sense. A few  important lemmas which are essential to solve the problems using the proposed method are proved. The advantage of this method is  that it uses appropriate initial conditions and finds the solution to the problems without any discretization, linearization, perturbation, or  any restrictive assumptions. Model examples are presented to demonstrate the applicability and effectiveness of the proposed method.  The obtained results reveal that the FRDTM is very effective and simple for solving linear and non-linear fractional partial differential equations. Finally, some graphical features are presented to give a visual interpretation of the solutions behaviour.