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New results for boundary value problems of Hadamard-type fractional differential inclusions and integral boundary conditions

Bashir Ahmad1*, Sotiris K Ntouyas2 and Ahmed Alsaedi1

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 2013, 2013:275  doi:10.1186/1687-2770-2013-275

Published: 13 December 2013

Abstract

In this paper, we study the existence of solutions for a fractional boundary value problem involving Hadamard-type fractional differential inclusions and integral boundary conditions. Our results include the cases for convex as well as non-convex valued maps and are based on standard fixed point theorems for multivalued maps. Some illustrative examples are also presented.

MSC: 34A60, 34A08.

Keywords:
Hadamard fractional derivative; integral boundary conditions; fixed point theorems