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Existence results for fractional integral inclusions via nonlinear alternative for contractive maps

Ahmed Alsaedi1, Sotiris K Ntouyas2, Bashir Ahmad1* and Hamed H Alsulami1

Author Affiliations

1 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

2 Department of Mathematics, University of Ioannina, Ioannina, 451 10, Greece

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Boundary Value Problems 2014, 2014:25  doi:10.1186/1687-2770-2014-25

Published: 30 January 2014

Abstract

In this paper, a new existence result is obtained for a fractional multivalued problem with fractional integral boundary conditions by applying a (Krasnoselskii type) fixed-point result for multivalued maps due to Petryshyn and Fitzpatric [Trans. Am. Math. Soc. 194:1-25, 1974]. The case for lower semi-continuous multivalued maps is also discussed. An example for the illustration of our main result is presented.

MSC: 34A60, 34A08.

Keywords:
fractional differential inclusions; nonlocal boundary conditions; fixed-point theorems