A new study on the existence and stability to a system of coupled higher-order nonlinear BVP of hybrid FDEs under the $ p $-Laplacian operator

Abdulwasea Alkhazzan; Wadhah Al-Sadi; Varaporn Wattanakejorn; Hasib Khan; Thanin Sitthiwirattham; Sina Etemad; Shahram Rezapour; Abdulwasea Alkhazzan; Wadhah Al-Sadi; Varaporn Wattanakejorn; Hasib Khan; Thanin Sitthiwirattham; Sina Etemad; Shahram Rezapour

doi:10.3934/math.2022782

AIMS Mathematics

2022, Volume 7, Issue 8: 14187-14207. doi: 10.3934/math.2022782

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A new study on the existence and stability to a system of coupled higher-order nonlinear BVP of hybrid FDEs under the $ p $-Laplacian operator

1.
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, Shannxi, China
2.
Department of Mathematics, College of Science, China University of Geoscience, Wuhan, China
3.
Department of Mathematics, College of Science, Sana'a University, Sana'a, Yemen
4.
Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand
5.
Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Dir Upper 18000, Khyber Pakhtunkhwa, Pakistan
6.
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
7.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Received: 05 February 2022 Revised: 21 April 2022 Accepted: 15 May 2022 Published: 30 May 2022
MSC : 34A08, 34A12

In this paper, we study a general system of fractional hybrid differential equations with a nonlinear $ \phi_p $-operator, and prove the existence of solution, uniqueness of solution and Hyers-Ulam stability. We use the Caputo fractional derivative in this system so that our system is more general and complex than other nonlinear systems studied before. To establish the results, Green functions are used to transform the considered hybrid boundary problem into a system of fractional integral equations. Then, with the help of the topological degree theorem, we derive some sufficient conditions that ensure the existence and uniqueness of solutions for the proposed system. Finally, an example is presented to show the validity and correctness of the obtained results.
- Hyers-Ulam stability,
- coupled system,
- existence of solution,
- the Caputo fractional derivative,
- Green function
Citation: Abdulwasea Alkhazzan, Wadhah Al-Sadi, Varaporn Wattanakejorn, Hasib Khan, Thanin Sitthiwirattham, Sina Etemad, Shahram Rezapour. A new study on the existence and stability to a system of coupled higher-order nonlinear BVP of hybrid FDEs under the $ p $-Laplacian operator[J]. AIMS Mathematics, 2022, 7(8): 14187-14207. doi: 10.3934/math.2022782

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Abstract

In this paper, we study a general system of fractional hybrid differential equations with a nonlinear $ \phi_p $-operator, and prove the existence of solution, uniqueness of solution and Hyers-Ulam stability. We use the Caputo fractional derivative in this system so that our system is more general and complex than other nonlinear systems studied before. To establish the results, Green functions are used to transform the considered hybrid boundary problem into a system of fractional integral equations. Then, with the help of the topological degree theorem, we derive some sufficient conditions that ensure the existence and uniqueness of solutions for the proposed system. Finally, an example is presented to show the validity and correctness of the obtained results.

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