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Mathematical Problems in Engineering
Volume 2013, Article ID 981526, 11 pages
Research Article

Existence and Numerical Solution of the Volterra Fractional Integral Equations of the Second Kind

1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
2Department of Mathematics, Faculty of Art & Sciences, Celal Bayar University, Muradiye Campus, 45047 Manisa, Turkey

Received 26 July 2013; Accepted 18 September 2013

Academic Editor: Hossein Jafari

Copyright © 2013 Abdon Atangana and Necdet Bildik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This work presents the possible generalization of the Volterra integral equation second kind to the concept of fractional integral. Using the Picard method, we present the existence and the uniqueness of the solution of the generalized integral equation. The numerical solution is obtained via the Simpson 3/8 rule method. The convergence of this scheme is presented together with numerical results.