Existence and stability results for nonlinear coupled singular fractional-order differential equations with time delay

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

doi:10.3934/math.2023804

AIMS Mathematics

2023, Volume 8, Issue 7: 15749-15772. doi: 10.3934/math.2023804

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Research article

Existence and stability results for nonlinear coupled singular fractional-order differential equations with time delay

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, Bandırma 10200, Balıkesir, Turkey
4.
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: 20 December 2022 Revised: 08 April 2023 Accepted: 19 April 2023 Published: 28 April 2023
MSC : 39B52, 39B72, 39B82

The objective of the manuscript is to build coupled singular fractional-order differential equations with time delay. To study the underline problem, an integral representation is initially discussed and the operator form of the solution is investigated using various supplementary hypotheses. Also, the existence and uniqueness of the considered problem are investigated by using the Lebesgue-dominated convergence theorem and some analysis results. Moreover, the stability analysis to determine the nature of the proposed model's solution is examined. Finally, two supportive examples are provided to demonstrate our analysis as applications.
- time delay,
- coupled fractional order differential equation,
- Lebesgue-dominated convergence theorem,
- Schaefer theorem,
- stability result
Citation: Hasanen A. Hammad, Hüseyin Işık, Manuel De la Sen. Existence and stability results for nonlinear coupled singular fractional-order differential equations with time delay[J]. AIMS Mathematics, 2023, 8(7): 15749-15772. doi: 10.3934/math.2023804

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Abstract

The objective of the manuscript is to build coupled singular fractional-order differential equations with time delay. To study the underline problem, an integral representation is initially discussed and the operator form of the solution is investigated using various supplementary hypotheses. Also, the existence and uniqueness of the considered problem are investigated by using the Lebesgue-dominated convergence theorem and some analysis results. Moreover, the stability analysis to determine the nature of the proposed model's solution is examined. Finally, two supportive examples are provided to demonstrate our analysis as applications.

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