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Journal of Function Spaces and Applications
Volume 2013, Article ID 428094, 13 pages
http://dx.doi.org/10.1155/2013/428094
Research Article

On Solutions of Fractional Order Boundary Value Problems with Integral Boundary Conditions in Banach Spaces

1Department of Mathematics, Faculty of Sciences, Alexandria University, Alexandria, Egypt
2Faculty of Sciences, Taibah University, Yanbu, Saudi Arabia
3Faculty of Mathematics and Computer Science, Adam Mickiewcz University, Umultowska 87, 61-614 Poznan, Poland

Received 28 August 2012; Accepted 6 April 2013

Academic Editor: Gennaro Infante

Copyright © 2013 Hussein A. H. Salem and Mieczysław Cichoń. 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

The object of this paper is to investigate the existence of a class of solutions for some boundary value problems of fractional order with integral boundary conditions. The considered problems are very interesting and important from an application point of view. They include two, three, multipoint, and nonlocal boundary value problems as special cases. We stress on single and multivalued problems for which the nonlinear term is assumed only to be Pettis integrable and depends on the fractional derivative of an unknown function. Some investigations on fractional Pettis integrability for functions and multifunctions are also presented. An example illustrating the main result is given.