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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 658617, 8 pages
http://dx.doi.org/10.1155/2013/658617
Research Article

On the Solvability of Caputo -Fractional Boundary Value Problem Involving -Laplacian Operator

Eastern Mediterranean University, Gazimagusa, Mersin 10, Turkey

Received 2 April 2013; Accepted 10 June 2013

Academic Editor: Nazim Idrisoglu Mahmudov

Copyright © 2013 Hüseyin Aktuğlu and Mehmet Ali Özarslan. 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 consider the model of a Caputo -fractional boundary value problem involving -Laplacian operator. By using the Banach contraction mapping principle, we prove that, under some conditions, the suggested model of the Caputo -fractional boundary value problem involving -Laplacian operator has a unique solution for both cases of and . It is interesting that in both cases solvability conditions obtained here depend on , , and the order of the Caputo -fractional differential equation. Finally, we illustrate our results with some examples.