THE EXISTENCE AND ULAM-HYERS STABILITY RESULTS FOR MULTI-POINT GENERALIZED CAPUTO FRACTIONAL BOUNDARY VALUE PROBLEMS
Makaleler > Tam Makale · 2025
Yazarlar: Fercan FİLİZ, Erbil ÇETİN
Journal of Applied Analysis & Computation, SCI Expanded İndekslerine Giren Dergi, Uluslararası, Wos, 2025, cilt 16, ss 757-778
DOI: 10.11948/20250157
Özet
This paper addresses a class of multi-point boundary value problems involvinggeneralized fractional derivatives with integral conditions. Specifically, we consider the following problem $\begin{aligned}& { }^c D_{a^{+}}^{\alpha, h} u(t)+f(t, u(t))=0, \quad t \in[a, b], \\& u^{(i)}(a)=0, i=0,1,2, \ldots, n-2, \\& u(b)=\sum\limits_{j=1}^{m-2} \beta_j \int_a^{\eta_j} g(s) u(s) d s+\sum\limits_{j=1}^{m-2} \lambda_j u\left(\eta_j\right) .\end{aligned}$ We establish necessary and sufficient conditions for the existence and uniqueness of solutionsto this problem. Our approach relies on the Banach fixed point theorem and Schaefer's fixedpoint theorem to prove the existence of solutions. Additionally, we introduce the conceptof Ulam-Hyers stability for this class of boundary value problems and provide a stabilityanalysis. To illustrate the applicability of our theoretical results, we present two concreteexamples.