A semi-analytical solutions of the multi-dimensional time-fractional Klein-Gordon equations using residual power series method

This study presents a novel approach to getting a semi-analytical solution to the multi-dimensional time-fractional linear and nonlinear Klein-Gordon equations with appropriate initial conditions using the residual power series method. The time-fractional derivative (beta) is used in the context of the Caputo approach. Some test examples of KGEs are considered to illustrate the validity and efficiency of the employed RPS method. The RPS solutions are compared with the exact solutions for beta = 2 to ensure the method's reliability and precision. The error bound and convergence analysis of the proposed method are also examined. The effects of the distinct values of fractional order beta is an element of (1, 2] on the behavior of the proposed equations are also discussed.