On the Existence of Solutions for a Fractional Differential Boundary Value Problem via Darbo-Type Fixed Point
Azerbaijan Journal of Mathematics, cilt.16, sa.2, ss.255-268, 2026 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 16 Sayı: 2
- Basım Tarihi: 2026
- Doi Numarası: 10.59849/2218-6816.2026.2.255
- Dergi Adı: Azerbaijan Journal of Mathematics
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
- Sayfa Sayıları: ss.255-268
- Anahtar Kelimeler: Caputo fractional derivative, generalized Proinov contrac-tion, measure of noncompactness
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- İstanbul Gelişim Üniversitesi Adresli: Evet
Özet
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.