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.
Highlights
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.Licensee MDPI, Basel, Switzerland.Elastic beam (EB) deflections are commonly known phenomena in science and engineering
The above findings inspired us in this study concerning the solutions’ existence and uniqueness with various types of Ulam stability results for the proposed discrete fractional elastic beam equation (FEBE) that is subject to the three-point boundary conditions (BCs) as follows: (
We show that Equation (48) is Hyers–U lam (HU) R stable
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. A few research studies that have been conducted on discrete fractional-order BVPs can be found in [34,35,36,37,38,39,40,41,42,43,44,45,46,47]. The above findings inspired us in this study concerning the solutions’ existence and uniqueness with various types of Ulam stability results for the proposed discrete fractional elastic beam equation (FEBE) that is subject to the three-point BCs as follows:. By using this solution, the existence and uniqueness conditions for the proposed discrete FEBE with three-point BCs (Equation (2)) are derived with the help of contraction mapping and the Brouwer fixed-point theorems.
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