Author(s)

Fatheah Alhendi^1*, Wafa Shammakh¹, Hind Al-Badrani²

¹Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia.
²Taibah University, Madinah, Saudi Arabia.

In this article, variational iteration method (VIM) and homotopy perturbation method (HPM) solve the nonlinear initial value problems of first-order fractional quadratic integro-differential equations (FQIDEs). We use the Caputo sense in this article to describe the fractional derivatives. The solutions of the problems are derived by infinite convergent series, and the results show that both methods are most convenient and effective.

Fractional Quadratic Integro-Differential Equations, Variational Iteration Method, Homotopy Perturbation Method

Alhendi, F. , Shammakh, W. and Al-Badrani, H. (2017) Numerical Solutions for Quadratic Integro-Differential Equations of Fractional Orders. Open Journal of Applied Sciences, 7, 157-170. doi: 10.4236/ojapps.2017.74014.