On fractional differential inclusions with anti-periodic type integral boundary conditions

Bashir Ahmad,Ahmed Alsaedi,Sotiris K Ntouyas

doi:10.1186/1687-2770-2013-82

Abstract

Abstract This paper investigates the existence of solutions for fractional differential inclusions of order q ∈ ( 2 , 3 ] 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.

Highlights

The topic of fractional differential equations and inclusions has recently emerged as a popular field of research due to its extensive development and applications in several disciplines such as physics, mechanics, chemistry, engineering, etc. [ – ]
For some recent results on fractional differential equations, see [ – ] and the references cited therein, whereas some recent work dealing with fractional differential inclusions can be found in [ – ]
We study a boundary value problem of fractional differential inclusions with anti-periodic type integral boundary conditions given by

Summary

Introduction

The topic of fractional differential equations and inclusions has recently emerged as a popular field of research due to its extensive development and applications in several disciplines such as physics, mechanics, chemistry, engineering, etc. [ – ]. If the multivalued map G is completely continuous with nonempty compact values, G is u.s.c. if and only if G has a closed graph, that is, xn –→ x∗, yn –→ y∗, yn ∈ G(xn) imply that y∗ ∈ G(x∗). A multivalued map G : [ , T] → P(R) with nonempty compact convex values is said to be measurable if for any x ∈ R, the function t –→ d x, F(t) = inf |x – y| : y ∈ F(t)

Results

Conclusion