Convergence of the generalized homotopy perturbation method for solving fractional order integro-differential equations

الملخص EN

In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations .

The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively.

We can easily obtain the solution from convergent the infinite series of HPM .

A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given.

Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.