Fast Adomian decomposition method for the Cauchy problem of the time-fractional reaction diffusion equation

The fractional reaction diffusion equation is one of the popularly used fractional partial differential equations in recent years. The fast Adomian decomposition method is used to obtain the solution of the Cauchy problem. Also, the analytical scheme is extended to the fractional one where the Taylor series is employed. In comparison with the classical Adomian decomposition method, the ratio of the convergence is increased. The method is more reliable for the fractional partial differential equations.