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The existence, uniqueness, and stability analysis of the discrete fractional three-point boundary value problem for the elastic beam equation

An elastic beam equation (EBEq) described by a fourth-order fractional difference equation is proposed in this work with three-point boundary conditions involving the Riemann-Liouville fractional difference operator. New sufficient conditions ensuring the solutions' existence and uniqueness of...

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Main Authors: Alzabut, Jehad, Selvam, A. George Maria, Dhineshbabu, R., Kaabar, Mohammed K. A.
Format: Article
Published: MDPI 2021
Subjects:
QA Mathematics
Online Access:http://eprints.um.edu.my/26676/
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spelling my.um.eprints.266762022-04-08T02:59:24Z http://eprints.um.edu.my/26676/ The existence, uniqueness, and stability analysis of the discrete fractional three-point boundary value problem for the elastic beam equation Alzabut, Jehad Selvam, A. George Maria Dhineshbabu, R. Kaabar, Mohammed K. A. QA Mathematics An elastic beam equation (EBEq) described by a fourth-order fractional difference equation is proposed in this work with three-point boundary conditions involving the Riemann-Liouville fractional difference operator. New sufficient conditions ensuring the solutions' existence and uniqueness of the proposed problem are established. The findings are obtained by employing properties of discrete fractional equations, Banach contraction, and Brouwer fixed-point theorems. Further, we discuss our problem's results concerning Hyers-Ulam (HU), generalized Hyers-Ulam (GHU), Hyers-Ulam-Rassias (HUR), and generalized Hyers-Ulam-Rassias (GHUR) stability. Specific examples with graphs and numerical experiment are presented to demonstrate the effectiveness of our results. MDPI 2021-05 Article PeerReviewed Alzabut, Jehad and Selvam, A. George Maria and Dhineshbabu, R. and Kaabar, Mohammed K. A. (2021) The existence, uniqueness, and stability analysis of the discrete fractional three-point boundary value problem for the elastic beam equation. Symmetry, 13 (5). ISSN 2073-8994, DOI https://doi.org/10.3390/sym13050789 <https://doi.org/10.3390/sym13050789>. 10.3390/sym13050789
institution Universiti Malaya
building UM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaya
content_source UM Research Repository
url_provider http://eprints.um.edu.my/
topic QA Mathematics
spellingShingle QA Mathematics
Alzabut, Jehad
Selvam, A. George Maria
Dhineshbabu, R.
Kaabar, Mohammed K. A.
The existence, uniqueness, and stability analysis of the discrete fractional three-point boundary value problem for the elastic beam equation
description An elastic beam equation (EBEq) described by a fourth-order fractional difference equation is proposed in this work with three-point boundary conditions involving the Riemann-Liouville fractional difference operator. New sufficient conditions ensuring the solutions' existence and uniqueness of the proposed problem are established. The findings are obtained by employing properties of discrete fractional equations, Banach contraction, and Brouwer fixed-point theorems. Further, we discuss our problem's results concerning Hyers-Ulam (HU), generalized Hyers-Ulam (GHU), Hyers-Ulam-Rassias (HUR), and generalized Hyers-Ulam-Rassias (GHUR) stability. Specific examples with graphs and numerical experiment are presented to demonstrate the effectiveness of our results.
format Article
author Alzabut, Jehad
Selvam, A. George Maria
Dhineshbabu, R.
Kaabar, Mohammed K. A.
author_facet Alzabut, Jehad
Selvam, A. George Maria
Dhineshbabu, R.
Kaabar, Mohammed K. A.
author_sort Alzabut, Jehad
title The existence, uniqueness, and stability analysis of the discrete fractional three-point boundary value problem for the elastic beam equation
title_short The existence, uniqueness, and stability analysis of the discrete fractional three-point boundary value problem for the elastic beam equation
title_full The existence, uniqueness, and stability analysis of the discrete fractional three-point boundary value problem for the elastic beam equation
title_fullStr The existence, uniqueness, and stability analysis of the discrete fractional three-point boundary value problem for the elastic beam equation
title_full_unstemmed The existence, uniqueness, and stability analysis of the discrete fractional three-point boundary value problem for the elastic beam equation
title_sort existence, uniqueness, and stability analysis of the discrete fractional three-point boundary value problem for the elastic beam equation
publisher MDPI
publishDate 2021
url http://eprints.um.edu.my/26676/
_version_ 1735409443442524160
score 13.159267

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