On the Existence of Solutions for a Fractional Differential Boundary Value Problem via Darbo-Type Fixed Point
Azerbaijan Journal of Mathematics, vol.16, no.2, pp.255-268, 2026 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 16 Issue: 2
- Publication Date: 2026
- Doi Number: 10.59849/2218-6816.2026.2.255
- Journal Name: Azerbaijan Journal of Mathematics
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
- Page Numbers: pp.255-268
- Keywords: Caputo fractional derivative, generalized Proinov contrac-tion, measure of noncompactness
- Open Archive Collection: AVESIS Open Access Collection
- Istanbul Gelisim University Affiliated: Yes
Abstract
In this work, we study the existence of solutions for a class of fractional boundary value problems involving the Caputo fractional derivative. Our approach is based on transforming the considered boundary value problems into an equivalent fixed-point equation by applying fixed-point results related to generalized Proinov-type contraction mappings defined through the measure of noncompactness. The obtained results substantially extend classical contraction principles and offer powerful tools for the analysis of nonlinear problems. An illustrative example is presented to demonstrate the significance and the applicability of the obtained results.