Abstract
We study a nonlinear three-point boundary value problem of sequential fractional differential inclusions of orderξ+1withn-1<ξ≤n,n≥2. Some new existence results for convex as well as nonconvex multivalued maps are obtained by using standard fixed point theorems. The paper concludes with an example.
Highlights
The topic of fractional differential equations has attracted a great attention in the recent years
We begin this section with some preliminary material on multivalued maps [24, 25] that we need in the sequel
Our strategy to deal with this problem is based on the nonlinear alternative of Leray-Schauder type together with the selection theorem of Bressan and Colombo [28] for lower semicontinuous maps with decomposable values
Summary
The topic of fractional differential equations has attracted a great attention in the recent years. The systematic development of theory, methods, and applications of fractional differential equations can be found in [1,2,3,4,5,6]. For some recent results on fractional differential equations and inclusions, see [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23] and the references cited therein. The present work is motivated by a recent paper of the authors [14], where the problem (1) was considered for a single-valued case.
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