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Mathematics
Volume 10
Issue 21
10.3390/math10214068
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Article

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

by
Ahmed M. A. El-Sayed
1,†,
Sheren A. Abd El-Salam
2,*,† and
Hind H. G. Hashem
1,†
1
Faculty of Science, Alexandria University, Alexandria 21544, Egypt
2
Faculty of Sciences, Damanhour University, Damanhour 22511, Egypt
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2022, 10(21), 4068; https://doi.org/10.3390/math10214068
Submission received: 18 September 2022 / Revised: 25 October 2022 / Accepted: 27 October 2022 / Published: 1 November 2022
Versions Notes

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−α,α) 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−α,α)

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MDPI and ACS Style

El-Sayed, A.M.A.; El-Salam, S.A.A.; Hashem, H.H.G. Development on a Fractional Hybrid Differential Inclusion with a Nonlinear Nonlocal Fractional-Order Integral Inclusion. Mathematics 2022, 10, 4068. https://doi.org/10.3390/math10214068

AMA Style

El-Sayed AMA, El-Salam SAA, Hashem HHG. Development on a Fractional Hybrid Differential Inclusion with a Nonlinear Nonlocal Fractional-Order Integral Inclusion. Mathematics. 2022; 10(21):4068. https://doi.org/10.3390/math10214068

Chicago/Turabian Style

El-Sayed, Ahmed M. A., Sheren A. Abd El-Salam, and Hind H. G. Hashem. 2022. "Development on a Fractional Hybrid Differential Inclusion with a Nonlinear Nonlocal Fractional-Order Integral Inclusion" Mathematics 10, no. 21: 4068. https://doi.org/10.3390/math10214068

APA Style

El-Sayed, A. M. A., El-Salam, S. A. A., & Hashem, H. H. G. (2022). Development on a Fractional Hybrid Differential Inclusion with a Nonlinear Nonlocal Fractional-Order Integral Inclusion. Mathematics, 10(21), 4068. https://doi.org/10.3390/math10214068

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