approximate solution for high order fractional integro-differential equations via an optimum parameter method

The most significant objective of this article is the adoption of a method with a free parameter known as “the optimum asymptotic homotopy method” which has been utilized in order to obtain solutions for integral differential equations of high-order non integer derivative. the process in this method is more favorable than “homotopy perturbation method” as it has a more rapid convergence compared to the mentioned method or even the similar methods. another advantage of this method is that the convergence rate is recognized as control area. it is worth mentioning that caputo derivative is adopted in this article. a number of instances are provided to better understand the method and its level of efficiency compared to other same methods.