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

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

doi:10.3934/math.2023433

AIMS Mathematics

2023, Volume 8, Issue 4: 8633-8649. doi: 10.3934/math.2023433

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

1.
Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, Buraydah 52571, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
3.
Department of Engineering Science, Bandırma Onyedi Eylül University, 10200 Bandırma, Balıkesir, Turkey
4.
Institut Supérieur d'Informatique et des Techniques de Communication, Université de Sousse, H. Sousse 4000, Tunisia
5.
China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
6.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa
7.
Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country, 48940-Leioa (Bizkaia), Spain

Received: 07 November 2022 Revised: 28 January 2023 Accepted: 01 February 2023 Published: 06 February 2023
MSC : 34A08, 34A12, 47H10, 54H25

The goal of this paper is to present a new class of contraction mappings, so-called $ \eta _{\theta }^{\ell } $-contractions. Also, in the context of partially ordered metric spaces, some coupled fixed-point results for $ \eta _{\theta }^{\ell } $-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.
- fractional differential equation,
- Atangana-Baleanu fractional operator,
- fixed point methodology,
- Riemann-Liouville fractional integral
Citation: Hasanen A. Hammad, Hüseyin Işık, Hassen Aydi, Manuel De la Sen. Fixed point approach to the Mittag-Leffler kernel-related fractional differential equations[J]. AIMS Mathematics, 2023, 8(4): 8633-8649. doi: 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 $ \eta _{\theta }^{\ell } $-contractions. Also, in the context of partially ordered metric spaces, some coupled fixed-point results for $ \eta _{\theta }^{\ell } $-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.

References

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