Existence results for fractional differential inclusions with three-point fractional integral boundary conditions

Xi Fu

doi:10.1186/1687-1847-2013-304

Abstract

This paper is concerned with fractional differential inclusions with three-point fractional integral boundary conditions. We consider the fractional differential inclusions under both convexity and nonconvexity conditions on the multivalued term. Some new existence results are obtained by using standard fixed point theorems. Two examples are given to illustrate the main results.MSC:34A60, 26A33, 34B15.

Highlights

Fractional differential equations have recently gained much importance and attention due to the fact that they have been proved to be valuable tools in the modeling of many physical phenomena [ – ]
Differential inclusions arise in the mathematical modeling of certain problems in economics, optimal control, etc. and are widely studied by many authors, see [, ] and the references therein
For some recent works on differential inclusions of fractional order, we refer the reader to the references [, – ]

Summary

Introduction

Fractional differential equations have recently gained much importance and attention due to the fact that they have been proved to be valuable tools in the modeling of many physical phenomena [ – ]. Motivated by the above papers, in this article, we study a new class of fractional boundary value problems, i.e., the following fractional differential inclusions with three-point fractional integral boundary conditions: cDαx(t) ∈ F(t, x(t), cDβ x(t)), t ∈ [ , ], < α ≤ , < β < , x( ) = , aIγ x(η) + bx( ) = c, < η < , ( )

Results

Conclusion