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.