The Natural Transform Decomposition Method for Solving Fractional Klein-Gordon Equation

Abstract

In this paper, a coupling of the natural transform method and the Admoian decomposition method called the natural transform decomposition method (NTDM), is utilized to solve the linear and nonlinear time-fractional Klein-Gordan equation. The (NTDM), is introduced to derive the approximate solutions in series form for this equation. Solutions have been drawn for several values of the time power. To identify the strength of the method, three examples are presented.

The Four-Dimensional Natural Transform Adomian Decomposition Method and (3+1)-Dimensional Fractional Coupled Burgers’ Equation

“…This method is utilized to address the various physical phenomena modeled by fractional PDEs, as demonstrated in several research works. For instance, it has been applied to solve a coupled system of nonlinear PDEs [35], analyze the fractional unsteady flow of a polytropic gas model [36], investigate the solution of fractional telegraph equations [37], solve the fractional coupled KdV equation [38], find the solution of fractional-order heat and wave equations [39], and solve the fractional Klein-Gordon equation [40], and the double natural transform method with the Adomian decomposition method was used to solve a singular one-dimensional Boussinesq equation in [41].…”