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.