Open Access Research

On fractional differential inclusions with anti-periodic type 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, 2013:82  doi:10.1186/1687-2770-2013-82

Published: 10 April 2013

Abstract

This paper investigates the existence of solutions for fractional differential inclusions of order <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/82/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/82/mathml/M1">View MathML</a> with anti-periodic type integral boundary conditions by means of some standard fixed point theorems for inclusions. Our results include the cases when the multivalued map involved in the problem has convex as well as non-convex values. The paper concludes with an illustrative example.

MSC: 34A60, 34A08.

Keywords:
fractional differential inclusions; anti-periodic; integral boundary conditions; fixed point theorems