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Existence Results for Sequential Riemann–Liouville and Caputo Fractional Differential Inclusions with Generalized Fractional Integral Conditions

by Jessada Tariboon 1,*,†, Sotiris K. Ntouyas 2,3,†, Bashir Ahmad 3,† and Ahmed Alsaedi 3,†
1
Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
2
Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
3
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
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(6), 1044; https://doi.org/10.3390/math8061044
Received: 7 May 2020 / Revised: 1 June 2020 / Accepted: 22 June 2020 / Published: 26 June 2020
Under different criteria, we prove the existence of solutions for sequential fractional differential inclusions containing Riemann–Liouville and Caputo type derivatives and supplemented with generalized fractional integral boundary conditions. Our existence results rely on the endpoint theory, the Krasnosel’skiĭ’s fixed point theorem for multivalued maps and Wegrzyk’s fixed point theorem for generalized contractions. We demonstrate the application of the obtained results with the help of examples. View Full-Text
Keywords: Riemann–Liouville fractional derivative; Caputo fractional derivative; inclusions; endpoint theory; generalized fractional integral; Krasnosel’skiĭ’s multi-valued fixed point theorem; Wegrzyk’s fixed point theorem Riemann–Liouville fractional derivative; Caputo fractional derivative; inclusions; endpoint theory; generalized fractional integral; Krasnosel’skiĭ’s multi-valued fixed point theorem; Wegrzyk’s fixed point theorem
MDPI and ACS Style

Tariboon, J.; Ntouyas, S.K.; Ahmad, B.; Alsaedi, A. Existence Results for Sequential Riemann–Liouville and Caputo Fractional Differential Inclusions with Generalized Fractional Integral Conditions. Mathematics 2020, 8, 1044.

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