Perturbation iteration transform method for solving fractional order integro-differential equation

In this study, the Perturbation Iteration transform method, namely PITM, is in short presented and implemented for solving a class of fractional integro-differential equations. The fractional derivative will be in the Atangana–Baleanu Caputo fractional derivative sense (ABC). The (PITM) is consists of merging Laplace transform method and the perturbation iteration algorithm (PIM). The proposed method furnish the solution in the form of a fastly convergent series. Some illustrative examples are presented to illustrate that the PITM is a powerful, efficient and accurate method and it can be enforced to other nonlinear problems.