Abstract
This paper is concerned with a class of fractional differential inclusions whose multivalued term depends on lower-order fractional derivative with fractional (non)separated boundary conditions. The cases of convex-valued and non-convex-valued right-hand sides are considered. Some existence results are obtained by using standard fixed point theorems. A possible generalization for the inclusion problem with integral boundary conditions is also discussed. Examples are given to illustrate the results.
Highlights
The subject of fractional differential equations has emerged as an important area of investigation
If a multivalued map F is completely continuous with nonempty compact values, F is upper semicontinuous if and only if F has a closed graph, that is, if xn → x∗ and yn → y∗, yn ∈ F xn implies y∗ ∈ F x∗ 28
From the proof of the above lemma, we notice that the solution 2.13 of the problem 2.12 does not depend on the parameter a2, that is to say, the parameter a2 is of arbitrary nature for this problem
Summary
The subject of fractional differential equations has emerged as an important area of investigation. Motivated by the papers cited above, in this paper, we consider the existence results for a new class of fractional differential inclusions of the form cDαx t ∈ F t, x t , cDβx t , a.e. t ∈ 0, T , 1.4 where cDα denotes the Caputo fractional derivative of order α, F : 0, 1 × R × R → 2R is a multivalued map, 1 < α ≤ 2, 0 < β ≤ 1, and T > 0. The results of this paper can to be generalized to the boundary value problems of fractional differential inclusions 1.4 with the following integral boundary conditions: a1x 0 b1 cDγ x 0 c1 g s, x s ds, a2x T b2 cDγ x T c2 h s, x s ds, a1x 0 b1x T c1 g s, x s ds, a2 cDγ x 0.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
