On the Ulam-Hyers-Rassias stability of two structures of discrete fractional three-point boundary value problems: Existence theory

Omar Choucha; Abdelkader Amara; Sina Etemad; Shahram Rezapour; Delfim F. M. Torres; Thongchai Botmart; Omar Choucha; Abdelkader Amara; Sina Etemad; Shahram Rezapour; Delfim F. M. Torres; Thongchai Botmart

doi:10.3934/math.2023073

AIMS Mathematics

2023, Volume 8, Issue 1: 1455-1474. doi: 10.3934/math.2023073

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Research article

On the Ulam-Hyers-Rassias stability of two structures of discrete fractional three-point boundary value problems: Existence theory

1.
Laboratory of Applied Mathematics, University of Kasdi Merbah, Ouargla 30000, Algeria
2.
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
3.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
4.
Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
5.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 24 August 2022 Revised: 27 September 2022 Accepted: 10 October 2022 Published: 21 October 2022
MSC : 26A33, 34A08, 34A12

We prove existence and uniqueness of solutions to discrete fractional equations that involve Riemann-Liouville and Caputo fractional derivatives with three-point boundary conditions. The results are obtained by conducting an analysis via the Banach principle and the Brouwer fixed point criterion. Moreover, we prove stability, including Hyers-Ulam and Hyers-Ulam-Rassias type results. Finally, some numerical models are provided to illustrate and validate the theoretical results.
- discrete fractional operators,
- stability,
- existence results,
- Banach principle
Citation: Omar Choucha, Abdelkader Amara, Sina Etemad, Shahram Rezapour, Delfim F. M. Torres, Thongchai Botmart. On the Ulam-Hyers-Rassias stability of two structures of discrete fractional three-point boundary value problems: Existence theory[J]. AIMS Mathematics, 2023, 8(1): 1455-1474. doi: 10.3934/math.2023073

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Abstract

We prove existence and uniqueness of solutions to discrete fractional equations that involve Riemann-Liouville and Caputo fractional derivatives with three-point boundary conditions. The results are obtained by conducting an analysis via the Banach principle and the Brouwer fixed point criterion. Moreover, we prove stability, including Hyers-Ulam and Hyers-Ulam-Rassias type results. Finally, some numerical models are provided to illustrate and validate the theoretical results.

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