Approximate analytical solutions of fractional reaction-diffusion equations

The homotopy analysis method (HAM) of S.J. Liao has proven useful in obtaining analytical/numerical solutions to various nonlinear differential equations. In this work, the HAM is employed to obtain the analytical/numerical solutions of the nonlinear reaction-diffusion equations with time-fractional derivatives. The fractional derivatives are described in the Caputo sense. This approach transforms the solution of nonlinear reaction-diffusion equations into the solution of a hierarchy of linear equations. The solution is simple yet highly accurate and compare favorably with the solutions obtained early in the literature.