Fixed point approach to the Mittag-Leffler kernel-related fractional differential equations

Hasanen A. Hammad; Hüseyin Işık; Hassen Aydi; Manuel De la Sen

doi:10.3934/math.2023433

Fixed point approach to the Mittag-Leffler kernel-related fractional differential equations

Hasanen A. Hammad^*, Hüseyin Işık, Hassen Aydi^*, Manuel De la Sen

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

The goal of this paper is to present a new class of contraction mappings, so-called (Equation presented)-contractions. Also, in the context of partially ordered metric spaces, some coupled fixed-point results for (Equation presented)-contraction mappings are introduced. Furthermore, to support our results, two examples are provided. Finally, the theoretical results are applied to obtain the existence of solutions to coupled fractional differential equations with a Mittag-Leffler kernel.

Original language	English
Pages (from-to)	8633-8649
Number of pages	17
Journal	AIMS Mathematics
Volume	8
Issue number	4
DOIs	https://doi.org/10.3934/math.2023433
Publication status	Published - 2023
Externally published	Yes

Keywords

Atangana-Baleanu fractional operator
Riemann-Liouville fractional integral
fixed point methodology
fractional differential equation

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10.3934/math.2023433

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abstract = "The goal of this paper is to present a new class of contraction mappings, so-called (Equation presented)-contractions. Also, in the context of partially ordered metric spaces, some coupled fixed-point results for (Equation presented)-contraction mappings are introduced. Furthermore, to support our results, two examples are provided. Finally, the theoretical results are applied to obtain the existence of solutions to coupled fractional differential equations with a Mittag-Leffler kernel.",

keywords = "Atangana-Baleanu fractional operator, Riemann-Liouville fractional integral, fixed point methodology, fractional differential equation",

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AU - Işık, Hüseyin

AU - Aydi, Hassen

AU - De la Sen, Manuel

PY - 2023

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KW - Atangana-Baleanu fractional operator

KW - Riemann-Liouville fractional integral

KW - fixed point methodology

KW - fractional differential equation

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Fixed point approach to the Mittag-Leffler kernel-related fractional differential equations

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Keywords

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