Existence Results for Caputo–Hadamard Nonlocal Fractional Multi-Order Boundary Value Problems

Rezapour, Shahram; Chikh, Salim Ben; Amara, Abdelkader; Ntouyas, Sotiris K.; Tariboon, Jessada; Etemad, Sina

doi:10.3390/math9070719

Open AccessArticle

Existence Results for Caputo–Hadamard Nonlocal Fractional Multi-Order Boundary Value Problems

by

Shahram Rezapour

^1,2

,

Salim Ben Chikh

³,

Abdelkader Amara

³

,

Sotiris K. Ntouyas

^4,5

,

Jessada Tariboon

^6,*

and

Sina Etemad

²

¹

Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404, Taiwan

²

Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 51368, Iran

³

Laboratory of Applied Mathematics, University of Kasdi Merbah Ouargla, Ouargla 30000, Algeria

⁴

Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

⁵

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

⁶

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.

Mathematics 2021, 9(7), 719; https://doi.org/10.3390/math9070719

Submission received: 4 March 2021 / Revised: 23 March 2021 / Accepted: 23 March 2021 / Published: 26 March 2021

(This article belongs to the Special Issue Nonlinear Differential Equations and Functional Analysis: Theory and Applications)

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Abstract

In this paper, we studied the existence results for solutions of a new class of the fractional boundary value problem in the Caputo–Hadamard settings. Moreover, boundary conditions of this fractional problem were formulated as the mixed multi-order Hadamard integro-derivative conditions. To prove the main existence results, we applied two well-known techniques in the topological degree and fixed point theories. Finally, we provide two examples to show the compatibility of our theoretical findings.

Keywords: Caputo–Hadamard derivative; condensing function; topological degree theory; fractional boundary value problem (FBVP)

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MDPI and ACS Style

Rezapour, S.; Chikh, S.B.; Amara, A.; Ntouyas, S.K.; Tariboon, J.; Etemad, S. Existence Results for Caputo–Hadamard Nonlocal Fractional Multi-Order Boundary Value Problems. Mathematics 2021, 9, 719. https://doi.org/10.3390/math9070719

AMA Style

Rezapour S, Chikh SB, Amara A, Ntouyas SK, Tariboon J, Etemad S. Existence Results for Caputo–Hadamard Nonlocal Fractional Multi-Order Boundary Value Problems. Mathematics. 2021; 9(7):719. https://doi.org/10.3390/math9070719

Chicago/Turabian Style

Rezapour, Shahram, Salim Ben Chikh, Abdelkader Amara, Sotiris K. Ntouyas, Jessada Tariboon, and Sina Etemad. 2021. "Existence Results for Caputo–Hadamard Nonlocal Fractional Multi-Order Boundary Value Problems" Mathematics 9, no. 7: 719. https://doi.org/10.3390/math9070719

APA Style

Rezapour, S., Chikh, S. B., Amara, A., Ntouyas, S. K., Tariboon, J., & Etemad, S. (2021). Existence Results for Caputo–Hadamard Nonlocal Fractional Multi-Order Boundary Value Problems. Mathematics, 9(7), 719. https://doi.org/10.3390/math9070719

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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Existence Results for Caputo–Hadamard Nonlocal Fractional Multi-Order Boundary Value Problems

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