The existence, uniqueness, and stability analysis of the discrete fractional three-point boundary value problem for the elastic beam equation
Document Type
Article
Publication Date
5-1-2021
Abstract
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.
Keywords
Riemann-Liouville fractional difference operator, Boundary value problem, Discrete fractional calculus, Existence and uniqueness, Ulam stability, Elastic beam problem
Divisions
MathematicalSciences
Funders
Prince Sultan University
Publication Title
Symmetry
Volume
13
Issue
5
Publisher
MDPI
Publisher Location
ST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND