Boundary Value Problems for Hilfer Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions

Wongcharoen, Athasit; Ntouyas, Sotiris K.; Tariboon, Jessada

doi:10.3390/math8111905

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Boundary Value Problems for Hilfer Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions

by

Athasit Wongcharoen

^1,†,

Sotiris K. Ntouyas

^2,3,†

and

Jessada Tariboon

^4,*,†

¹

Department of Mechanical Engineering Technology, College of Industrial Engineering Technology, 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 Mathematices, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

⁴

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.

^†

These authors contributed equally to this work.

Mathematics 2020, 8(11), 1905; https://doi.org/10.3390/math8111905

Submission received: 2 October 2020 / Revised: 26 October 2020 / Accepted: 28 October 2020 / Published: 31 October 2020

(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications)

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Abstract

In this paper, we study boundary value problems for differential inclusions, involving Hilfer fractional derivatives and nonlocal integral boundary conditions. New existence results are obtained by using standard fixed point theorems for multivalued analysis. Examples illustrating our results are also presented.

Keywords: Hilfer fractional derivative; Riemann–Liouville fractional derivative; Caputo fractional derivative; boundary value problems; existence; fixed point theory

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MDPI and ACS Style

Wongcharoen, A.; Ntouyas, S.K.; Tariboon, J. Boundary Value Problems for Hilfer Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions. Mathematics 2020, 8, 1905. https://doi.org/10.3390/math8111905

AMA Style

Wongcharoen A, Ntouyas SK, Tariboon J. Boundary Value Problems for Hilfer Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions. Mathematics. 2020; 8(11):1905. https://doi.org/10.3390/math8111905

Chicago/Turabian Style

Wongcharoen, Athasit, Sotiris K. Ntouyas, and Jessada Tariboon. 2020. "Boundary Value Problems for Hilfer Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions" Mathematics 8, no. 11: 1905. https://doi.org/10.3390/math8111905

APA Style

Wongcharoen, A., Ntouyas, S. K., & Tariboon, J. (2020). Boundary Value Problems for Hilfer Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions. Mathematics, 8(11), 1905. https://doi.org/10.3390/math8111905

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Boundary Value Problems for Hilfer Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions

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