Numerical solution of fractional integro-differential equations by a hybrid collocation method

Fractional integro-differential equations have been recently solved by many methods, such as Adomian decomposition method, differential transform method, collocation method and Taylor expansion approach. In this paper a hybrid collocation method is used which combines a non-polynomial collocation used on the first subinterval and graded piecewise polynomial collocation used on the rest of the interval. A theoretical analysis for the convergence order of the method is presented. Some numerical examples are given which confirm the theoretical results.