Hybrid System of Proportional Hilfer-Type Fractional Differential Equations and Nonlocal Conditions with Respect to Another Function

Ntouyas, Sotiris K.; Wongsantisuk, Phollakrit; Samadi, Ayub; Tariboon, Jessada

doi:10.3390/math12071071

Open AccessArticle

Hybrid System of Proportional Hilfer-Type Fractional Differential Equations and Nonlocal Conditions with Respect to Another Function

¹

Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece

²

Department of Electronics Engineering Technology, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand

³

Department of Mathematics, Miyaneh Branch, Islamic Azad University, Miyaneh 5315836511, Iran

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.

Mathematics 2024, 12(7), 1071; https://doi.org/10.3390/math12071071

Submission received: 15 March 2024 / Revised: 29 March 2024 / Accepted: 31 March 2024 / Published: 2 April 2024

(This article belongs to the Special Issue Recent Investigations of Differential and Fractional Equations and Inclusions, 3rd Edition)

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Abstract

In this paper, a new class of coupled hybrid systems of proportional sequential

ψ

-Hilfer fractional differential equations, subjected to nonlocal boundary conditions were investigated. Based on a generalization of the Krasnosel’ski

\overset{˘}{i}

’s fixed point theorem due to Burton, sufficient conditions were established for the existence of solutions. A numerical example was constructed illustrating the main theoretical result. For special cases of the parameters involved in the system many new results were covered. The obtained result is new and significantly contributes to existing results in the literature on coupled systems of proportional sequential

ψ

-Hilfer fractional differential equations.

Keywords: coupled system; Hilfer fractional proportional derivative; nonlocal conditions; fixed-point theorem

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MDPI and ACS Style

Ntouyas, S.K.; Wongsantisuk, P.; Samadi, A.; Tariboon, J. Hybrid System of Proportional Hilfer-Type Fractional Differential Equations and Nonlocal Conditions with Respect to Another Function. Mathematics 2024, 12, 1071. https://doi.org/10.3390/math12071071

AMA Style

Ntouyas SK, Wongsantisuk P, Samadi A, Tariboon J. Hybrid System of Proportional Hilfer-Type Fractional Differential Equations and Nonlocal Conditions with Respect to Another Function. Mathematics. 2024; 12(7):1071. https://doi.org/10.3390/math12071071

Chicago/Turabian Style

Ntouyas, Sotiris K., Phollakrit Wongsantisuk, Ayub Samadi, and Jessada Tariboon. 2024. "Hybrid System of Proportional Hilfer-Type Fractional Differential Equations and Nonlocal Conditions with Respect to Another Function" Mathematics 12, no. 7: 1071. https://doi.org/10.3390/math12071071

APA Style

Ntouyas, S. K., Wongsantisuk, P., Samadi, A., & Tariboon, J. (2024). Hybrid System of Proportional Hilfer-Type Fractional Differential Equations and Nonlocal Conditions with Respect to Another Function. Mathematics, 12(7), 1071. https://doi.org/10.3390/math12071071

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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Hybrid System of Proportional Hilfer-Type Fractional Differential Equations and Nonlocal Conditions with Respect to Another Function

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