The Homotopy Analysis Method to Solve Time Fractional Partial Differential Equations

In this letter, we apply the homotopy analysis method (HAM) to obtain analytical solutions of the time fractional Klein-Gordon equation with variable coefficients, where the fractional derivatives are Caputo sense. The applications of the HAM were extended to derive analytical solutions in the form of a series with easily computed terms for these generalized fractional equations. A example is given to show the efficiency of the method, and it is shown that the HAM in solving the time fractional Klein-Gordon equation can be very precision.