A new analytical method to solve Klein-Gordon equations by using homotopy perturbation Mohand transform method

Abstract

In this paper, we will study about Fractional-order partial differential equations in Mathematical Science and we will introduce and analyse fractional calculus with an integral operator that contains the Caputo- Fabrizio’s fractional-order derivative. The advanced method is an appropriate union of the new integral transform named as ‘Mohand transform’ and the homotopy perturbation method. Some numerical examples are used to communicate the generality and clarity of the proposed method.We will also find the analytical solution of the linear and non-linear Klein –Gordan equation which originate in quantum field theory. The homotopy perturbation Mohand transform method (HPMTM) is a merged form of Mohand transform, homotopy perturbation method, and He’s polynomials. Some numerical examples are used to indicate the generality and clarity of the proposed method.