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Article

Boundary Value Problems for ψ-Hilfer Type Sequential Fractional Differential Equations and Inclusions with Integral Multi-Point Boundary Conditions

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Department of Social and Applied Science, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
2
Department of Mathematics, University of Ioannina, 45110 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
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Department of Mathematics, Miyaneh Branch, Islamic Azad University, Miyaneh, Iran
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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
*
Author to whom correspondence should be addressed.
Academic Editor: Andrey Amosov
Received: 23 March 2021 / Revised: 25 April 2021 / Accepted: 26 April 2021 / Published: 28 April 2021
(This article belongs to the Special Issue Nonlinear Boundary Value Problems and Their Applications)
In the present article, we study a new class of sequential boundary value problems of fractional order differential equations and inclusions involving ψ-Hilfer fractional derivatives, supplemented with integral multi-point boundary conditions. The main results are obtained by employing tools from fixed point theory. Thus, in the single-valued case, the existence of a unique solution is proved by using the classical Banach fixed point theorem while an existence result is established via Krasnosel’skiĭ’s fixed point theorem. The Leray–Schauder nonlinear alternative for multi-valued maps is the basic tool to prove an existence result in the multi-valued case. Finally, our results are well illustrated by numerical examples. View Full-Text
Keywords: fractional differential equations; fractional differential inclusions; Hilfer fractional derivative; Riemann–Liouville fractional derivative; Caputo fractional derivative; boundary value problems; existence and uniqueness; fixed point theory fractional differential equations; fractional differential inclusions; Hilfer fractional derivative; Riemann–Liouville fractional derivative; Caputo fractional derivative; boundary value problems; existence and uniqueness; fixed point theory
MDPI and ACS Style

Sitho, S.; Ntouyas, S.K.; Samadi, A.; Tariboon, J. Boundary Value Problems for ψ-Hilfer Type Sequential Fractional Differential Equations and Inclusions with Integral Multi-Point Boundary Conditions. Mathematics 2021, 9, 1001. https://0-doi-org.brum.beds.ac.uk/10.3390/math9091001

AMA Style

Sitho S, Ntouyas SK, Samadi A, Tariboon J. Boundary Value Problems for ψ-Hilfer Type Sequential Fractional Differential Equations and Inclusions with Integral Multi-Point Boundary Conditions. Mathematics. 2021; 9(9):1001. https://0-doi-org.brum.beds.ac.uk/10.3390/math9091001

Chicago/Turabian Style

Sitho, Surang, Sotiris K. Ntouyas, Ayub Samadi, and Jessada Tariboon. 2021. "Boundary Value Problems for ψ-Hilfer Type Sequential Fractional Differential Equations and Inclusions with Integral Multi-Point Boundary Conditions" Mathematics 9, no. 9: 1001. https://0-doi-org.brum.beds.ac.uk/10.3390/math9091001

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