Adomian Decomposition Method for Solving Fractional Time-Klein-Gordon Equations Using Maple

Adomian decomposition is a semi-analytical approach to solving ordinary and partial differential equations. This study aims to apply the Adomian De-composition Technique to obtain analytic solutions for linear and nonlinear time-fractional Klein-Gordon equations. The fractional derivatives are computed according to Caputo. Examples are provided. The findings show the explicitness, efficacy, and correctness of the used approach. Approximate solutions acquired by the decomposition method have been numerically assessed, given in the form of graphs and tables, and then these answers are compared with the actual solutions. The Adomian decomposition approach, which was used in this study, is a widely used and convergent method for the solutions of linear and non-linear time fractional Klein-Gordon equation.