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Open AccessFeature PaperArticle

On a Generalized Langevin Type Nonlocal Fractional Integral Multivalued Problem

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Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
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Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1015; https://doi.org/10.3390/math7111015
Received: 29 August 2019 / Revised: 17 October 2019 / Accepted: 21 October 2019 / Published: 25 October 2019
We establish sufficient criteria for the existence of solutions for a nonlinear generalized Langevin-type nonlocal fractional-order integral multivalued problem. The convex and non-convex cases for the multivalued map involved in the given problem are considered. Our results rely on Leray–Schauder nonlinear alternative for multivalued maps and Covitz and Nadler’s fixed point theorem. Illustrative examples for the main results are included. View Full-Text
Keywords: differential inclusions; Caputo-type fractional derivative; fractional integral; existence; fixed point differential inclusions; Caputo-type fractional derivative; fractional integral; existence; fixed point
MDPI and ACS Style

Alsaedi, A.; Ahmad, B.; Alghanmi, M.; Ntouyas, S.K. On a Generalized Langevin Type Nonlocal Fractional Integral Multivalued Problem. Mathematics 2019, 7, 1015.

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