Fractional coupled decomposition approach for the solution of a linear Klein–Gordon equation

Abstract

Abstract In this article, the solution of the time-fractional linear Klein-Gordon Equation (TFLKGE) is considered. This is in combination with Laplace Decomposition Method (LDM) and Fractional Complex Transform (FCT), herein referred to as FCLDM. In contrast with the standard LDM, this proposed approach demonstrates a feasible improvement and efficiency in use. Considerations are made Illustratively using some examples, and a closed solution of the problem is obtained with ease. The FCLDM is recommended for physical modeling of real-life problems both in pure and applied sciences and for strongly non-linear differential models.