Reliable Algorithm for Solving Integro-Differential Equations of Fractional Order Using Homotopy Analysis Method

In this paper, a powerful algorithm of the homotopy analysis method were developed and used to find theapproximate solution of integro-differential equations of fractional order. Which consist of fractional order ofdifferentiation and fractional order of integration. The fractional derivative is described in the Caputo sense and the fractional integration is described in the Riemann-Liouville sense. In addition some examples are used to illustrate the accuracy and validity of this approach.