Convergence analysis of homotopy perturbation method for Volterra integro-differential equations of fractional order

Based on the homotopy perturbation method (HPM), a general analytical approach for obtaining approximate series solutions to Volterra integro-differential equations of fractional order is proposed. The approximate solutions are calculated in the form of a convergent series with easily computable components. In this paper, the uniqueness of the obtained solution and the convergence properties of the approach are studied. Some examples are presented, to verify convergence, and illustrating the efficiency and simplicity of the approach.