Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 709106, 14 pages
http://dx.doi.org/10.1155/2012/709106
Research Article

Monte-Carlo Galerkin Approximation of Fractional Stochastic Integro-Differential Equation

Abdallah Ali Badr1 and Hanan Salem El-Hoety2

1Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt
2Department of Mathematics, Faculty of Science, Garyounis University, Benghazi, Libya

Received 30 November 2011; Accepted 2 February 2012

Academic Editor: Francesco Pellicano

Copyright © 2012 Abdallah Ali Badr and Hanan Salem El-Hoety. 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.

Abstract

A stochastic differential equation, SDE, describes the dynamics of a stochastic process defined on a space-time continuum. This paper reformulates the fractional stochastic integro-differential equation as a SDE. Existence and uniqueness of the solution to this equation is discussed. A numerical method for solving SDEs based on the Monte-Carlo Galerkin method is presented.