Existence and stability results for a coupled system of impulsive fractional differential equations with Hadamard fractional derivatives

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

doi:10.3934/math.2023350

AIMS Mathematics

2023, Volume 8, Issue 3: 6913-6941. doi: 10.3934/math.2023350

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Research article

Existence and stability results for a coupled system of impulsive fractional differential equations with Hadamard fractional derivatives

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.
Institut Supérieur d'Informatique et des Techniques de Communication, Université de Sousse, H. Sousse 4000, Tunisia
4.
China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
5.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa
6.
Department of Engineering Science, Bandırma Onyedi Eylül University, Bandırma 10200, Balıkesir, Turkey
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: 30 October 2022 Revised: 26 December 2022 Accepted: 29 December 2022 Published: 10 January 2023
MSC : 34A08, 34A12, 47H10

The purpose of this study is to give some findings on the existence, uniqueness, and Hyers-Ulam stability of the solution of an implicit coupled system of impulsive fractional differential equations possessing a fractional derivative of the Hadamard type. The existence and uniqueness findings are obtained using a fixed point theorem of the type of Kransnoselskii. In keeping with this, many forms of Hyers-Ulam stability are examined. Ultimately, to support main results, an example is provided.
- impulsive effect,
- existence solution,
- fixed point technique,
- Hadamard fractional derivative,
- Hyers-Ulam stability
Citation: Hasanen A. Hammad, Hassen Aydi, Hüseyin Işık, Manuel De la Sen. Existence and stability results for a coupled system of impulsive fractional differential equations with Hadamard fractional derivatives[J]. AIMS Mathematics, 2023, 8(3): 6913-6941. doi: 10.3934/math.2023350

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Abstract

The purpose of this study is to give some findings on the existence, uniqueness, and Hyers-Ulam stability of the solution of an implicit coupled system of impulsive fractional differential equations possessing a fractional derivative of the Hadamard type. The existence and uniqueness findings are obtained using a fixed point theorem of the type of Kransnoselskii. In keeping with this, many forms of Hyers-Ulam stability are examined. Ultimately, to support main results, an example is provided.

References

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