Mohammad Zurigat, Shaher Momani and Ahmad Alawneh, Homotopy analysis method for systems of fractional integro-differential equations, Proceeding of The Fourth International Workshop of Advanced Computation for Engineering Applications, Jordan, (2008) 106-111.

In this article, based on the homotopy analysis method (HAM), a new a nalytic technique is proposed to solve systems of fractional integro-differential e quations. Comparing with the exact solution, the HAM provides us with a simple way to adjust and control the convergence region of the series solution by introducing an auxilia ry parameter h . Four examples are tested using the proposed technique. It is shown that the solutions obtained by the Adomian decomposition method (ADM) are only special cases of the HAM solutions. The present work shows the validity and great potential of the homotopy analysis method for solving linear and nonlinear systems of fractiona l integro-differential equations. The basic idea described in this article is expected to be further employed to solve other similar nonlinear problems in fractional calculus.