Numerical Solution of Time Fractional Klein-Gordon Equation in Framework of the Yang-Abdel-Cattani Fractional Derivative Operator

This paper investigates the analytical results of both linear and nonlinear time-fractional KleinGordon equations using the novel Yang-Abdel-Cattani derivative operator. In order to solve the proposed time-fractional Klein-Gordon equations, we applied the Laplace Adomian decomposition technique. The effectiveness of this operator is demonstrated through three test problems. These include both linear and nonlinear time-fractional Klein-Gordon equations. Furthermore, the influence of different fractional Brownian motion values on the solution profiles is analyzed and presented graphically