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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
DOI: 10.3934/mbe.2022505
ISSN: 1547-1063
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Appears in Collections:CIDMA - Artigos
FAAG - Artigos

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