Riv. Mat. Univ. Parma, Vol. 11, No. 2, 2020

Noureddine Bouteraa [a] and Slimane Benaicha [a]

Existence results for fractional differential inclusion with nonlocal boundary conditions

Pages: 181-206
Received: 15 July 2018
Accepted in revised form: 3 September 2019
Mathematics Subject Classification (2010): 47H10, 26A33, 34A08.
Keywords: Fractional differential inclusion, Existence, Nonlocal boundary, Fixed point theorem.
Authors address:
[a]: Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), University of Oran1, Ahmed Benbella, Algeria

Full Text (PDF)

Abstract: This paper deals with the existence of solutions for nonlinear singular higher fractional differential inclusions supplemented with multi-point boundary conditions. Firstly, we investigate it for \(L^{1}-\)Carathéodory convex, compact valued, multifunctions. Secondly, we investigate it for the case of not necessarily convex valued multifunctions via some conditions by applying Schaefer's fixed point theorem combined with the selection theorem due to Bressan and Colombo. Finally, we investigate it for nonconvex valued multifunctions via a fixed point theorem for multivalued maps due to Covitz and Nadler. Two illustrative examples are presented at the end of the paper to illustrate the validity of our results.

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