Homotopy analysis method for higher-order fractional integro-differential equations

In this paper, we present the homotopy analysis method (shortly HAM) for obtaining the numerical solutions of higher‐order fractional integro‐differential equations with boundary conditions. The series solution is developed and the recurrence relations are given explicitly. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary conditions. The comparison of the results obtained by the HAM with the exact solutions is made, the results reveal that the HAM is very effective and simple. The HAM contains the auxiliary parameter $h$ , which provides us with a simple way to adjust and control the convergence region of series solution.