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http://hdl.handle.net/10773/35004
Title: | On the solution and Ulam-Hyers-Rassias stability of a Caputo fractional boundary value problem |
Author: | Castro, Luís P. Silva, Anabela S. |
Keywords: | Boundary value problem Caputo fractional derivative Fixed point Ulam-Hyers stability Ulam-Hyers-Rassias stability |
Issue Date: | 28-Jul-2022 |
Publisher: | AIMS Press |
Abstract: | In this paper, we investigate a class of boundary value problems involving Caputo fractional derivative CDα a of order α ∈ (2, 3), and the usual derivative, of the form (CDαa x)(t) + p(t)x 0 (t) + q(t)x(t) = g(t), a ≤ t ≤ b, for an unknown x with x(a) = x 0 (a) = x(b) = 0, and p, q, g ∈ C 2 ([a, b]). The proposed method uses certain integral inequalities, Banach’s Contraction Principle and Krasnoselskii’s Fixed Point Theorem to identify conditions that guarantee the existence and uniqueness of the solution (for the problem under study) and that allow the deduction of Ulam-Hyers and Ulam-Hyers-Rassias stabilities. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/35004 |
DOI: | 10.3934/mbe.2022505 |
ISSN: | 1547-1063 |
Publisher Version: | https://www.aimspress.com/article/doi/10.3934/mbe.2022505 |
Appears in Collections: | CIDMA - Artigos FAAG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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CastroSilva_mbe.pdf | 649.47 kB | Adobe PDF | View/Open |
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