The existence and stability results of multi-order boundary value problems involving Riemann-Liouville fractional operators

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

doi:10.3934/math.2023574

AIMS Mathematics

2023, Volume 8, Issue 5: 11325-11349. doi: 10.3934/math.2023574

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The existence and stability results of multi-order boundary value problems involving Riemann-Liouville fractional operators

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.
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: 26 October 2022 Revised: 26 February 2023 Accepted: 07 March 2023 Published: 13 March 2023
MSC : 34A08, 34A12

In this paper, a general framework for the fractional boundary value problems is presented. The problem is created by Riemann-Liouville type two-term fractional differential equations with a fractional bi-order setup. Moreover, the boundary conditions of the suggested system are considered as mixed Riemann-Liouville integro-derivative conditions with four different orders, which it cover a variety of specific instances previously researched. Further, the provided problem's Hyers-Ulam stability and the possibility of a fixed-point approach solution are both investigated. Finally, to support our theoretical findings, an example is developed.
- Riemann-Liouville fractional derivative,
- coupled fractional boundary value problem,
- fixed point,
- Hyers-Ulam stability
Citation: Hasanen A. Hammad, Hassen Aydi, Manuel De la Sen. The existence and stability results of multi-order boundary value problems involving Riemann-Liouville fractional operators[J]. AIMS Mathematics, 2023, 8(5): 11325-11349. doi: 10.3934/math.2023574

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Abstract

In this paper, a general framework for the fractional boundary value problems is presented. The problem is created by Riemann-Liouville type two-term fractional differential equations with a fractional bi-order setup. Moreover, the boundary conditions of the suggested system are considered as mixed Riemann-Liouville integro-derivative conditions with four different orders, which it cover a variety of specific instances previously researched. Further, the provided problem's Hyers-Ulam stability and the possibility of a fixed-point approach solution are both investigated. Finally, to support our theoretical findings, an example is developed.

References

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