THE EXISTENCE AND ULAM-HYERS STABILITY RESULTS FOR MULTI-POINT GENERALIZED CAPUTO FRACTIONAL BOUNDARY VALUE PROBLEMS

Fercan Filiz; Erbil Çetin

doi:10.11948/20250157

2026 Volume 16 Issue 2

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Fercan Filiz, Erbil Çetin. THE EXISTENCE AND ULAM-HYERS STABILITY RESULTS FOR MULTI-POINT GENERALIZED CAPUTO FRACTIONAL BOUNDARY VALUE PROBLEMS[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 757-778. doi: 10.11948/20250157

Citation:

Fercan Filiz, Erbil Çetin. THE EXISTENCE AND ULAM-HYERS STABILITY RESULTS FOR MULTI-POINT GENERALIZED CAPUTO FRACTIONAL BOUNDARY VALUE PROBLEMS[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 757-778. doi: 10.11948/20250157

THE EXISTENCE AND ULAM-HYERS STABILITY RESULTS FOR MULTI-POINT GENERALIZED CAPUTO FRACTIONAL BOUNDARY VALUE PROBLEMS

Fercan Filiz^1,,
Erbil Çetin^1, ,

1.
Department of Mathematics, Faculty of Science, Ege University, 35100 Bornova, Izmir, Turkey

Author Bio: Email: fercanfilizz@gmail.com(F. Filiz)
Corresponding author: Email: erbil.cetin@ege.edu.tr(E. Çetin)

Abstract

Abstract

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.
- Boundary value problem /
- generalized Caputo fractional derivative and integral /
- Green's function /
- fixed point theorem /
- existence and uniqueness of the solution
MSC: 26A33, 34K10, 34K37

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References

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