A homotopy perturbation method for fractional-order advection-diffusion-reaction boundary-value problems

Abstract

In this paper we describe the application of the homotopy perturbation method (HPM) to two-point boundary-value problems with fractional-order derivatives of Caputo-type. We show that HPM is equivalent to the semi-analytical Adomian decomposition method when applied to a class of nonlinear fractional advection-diffusion-reaction models. A general expression is derived for the coefficients in the HPM series solution. Numerical experiments are given to demonstrate several properties of HPM, such as its dependence on the fractional order and the parameters in the model. In the case of more than one solution, HPM has difficulties to find the second solution in the model. Another example is given for which HPM seems to converge to a non-existing solution.