Development on a Fractional Hybrid Differential Inclusion with a Nonlinear Nonlocal Fractional-Order Integral Inclusion

Ahmed M. A. El-Sayed, Sheren A. Abd El-Salam () and Hind H. G. Hashem
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Ahmed M. A. El-Sayed: Faculty of Science, Alexandria University, Alexandria 21544, Egypt
Sheren A. Abd El-Salam: Faculty of Sciences, Damanhour University, Damanhour 22511, Egypt
Hind H. G. Hashem: Faculty of Science, Alexandria University, Alexandria 21544, Egypt

Mathematics, 2022, vol. 10, issue 21, 1-14

Abstract: In this article, we consider a Riemann–Liouville fractional-order nonlinear hybrid delay differential inclusion with a nonlinear set-valued nonlocal integral condition of fractional order. We prove some existence and uniqueness results in C ( I , R ) . We also study the continuous dependence of the solutions on the two sets of selections of the two set-valued functions, considered in our problem, and on some other parameters. Finally, to validate our results, we present an example and some particular cases.

Keywords: Riemann–Liouville derivative and integrals; hybrid differential inclusion; multivalued nonlocal integral condition of fractional order; nonlinear alternative of Leray–Schauder type; continuous dependency; conjugate order (1??,?) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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