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Mathematical Problems in Engineering
Volume 2012, Article ID 329575, 11 pages
http://dx.doi.org/10.1155/2012/329575
Research Article

A Numerical Algorithm for Solving a Four-Point Nonlinear Fractional Integro-Differential Equations

1Department of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha 410073, China
2State key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China

Received 28 April 2012; Accepted 11 July 2012

Academic Editor: Hung Nguyen-Xuan

Copyright © 2012 Er Gao et al. 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

We provide a new algorithm for a four-point nonlocal boundary value problem of nonlinear integro-differential equations of fractional order 𝑞(1,2] based on reproducing kernel space method. According to our work, the analytical solution of the equations is represented in the reproducing kernel space which we construct and so the n-term approximation. At the same time, the n-term approximation is proved to converge to the analytical solution. An illustrative example is also presented, which shows that the new algorithm is efficient and accurate.