Existence and stability results for discrete fractional three-point boundary value problems

Eralp Işıksungur, Buse; Topal, Fatma Serap

doi:10.30495/maca.2024.2029404.1100

Existence and stability results for discrete fractional three-point boundary value problems

10.30495/maca.2024.2029404.1100

Volume 6, Issue 2
Spring 2024

Pages 17-31

Mathematical Analysis and its Contemporary Applications

Document Type : Original Article

Authors

Buse Eralp Işıksungur

Fatma Serap Topal

Department of Mathematics, Ege University, 35100 Bornova, Izmir, Turkey

Abstract

In this study, firstly we obtain the existing results for the following three-point boundary value problem
\begin{align*}
- \nabla^{\mu+1}y(t)=Ay(t)+f(t,y(t)), \ t \in \mathbb{N}_{a+2}^{b} \\
y(a+1)=0,\ \ \ y(b)=\delta \nabla y(\nu) \hspace{1cm}
\end{align*}
$0<\mu<1$, $A:\mathbb{C}(\mathbb{N}_{a+2}^{b},\mathbb{R})\longrightarrow \mathbb{R}$, $f:\mathbb{N}_{a+2}^{b}\times \mathbb{R}\longrightarrow \mathbb{R}$, by using the Brouwer fixed point theorem and the Banach fixed point theorem. Furthermore, we have established the stability of this problem in the sense of Hyers and Ulam. Examples are given which illustrate the effectiveness of the theoretical results.

Keywords

Existence of solutions

Discrete fractional equations

Ulam-Hyers stability

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