Analytical study of time-fractional order Klein–Gordon equation

In this article, we study an approximate analytical solution of linear and nonlinear time-fractional order Klein–Gordon equations by using a recently developed semi analytical method referred as fractional reduced differential transform method with appropriate initial condition. In the study of fractional Klein–Gordon equation, fractional derivative is described in the Caputo sense. The validity and efficiency of the aforesaid method are illustrated by considering three computational examples. The solution profile behavior and effects of different fraction Brownian motion on solution profile of the three numerical examples are shown graphically.