On the Fixed Point Theorem for Large Contraction Mappings with Applications to Delay Fractional Differential Equations
Fractal and Fractional, cilt.8, sa.12, 2024 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 8 Sayı: 12
- Basım Tarihi: 2024
- Doi Numarası: 10.3390/fractalfract8120703
- Dergi Adı: Fractal and Fractional
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Anahtar Kelimeler: Caputo operator, Chatterjea’s map, complete metric space, fixed point, large contraction
- Van Yüzüncü Yıl Üniversitesi Adresli: Evet
Özet
This paper explores a new class of mappings and presents several fixed-point results for these mappings. We define these mappings by combining well-known mappings in the literature, specifically the large contraction mapping and Chatterjea’s mapping. This combination allows us to achieve significant fixed-point results in complete metric spaces, both in a continuous and a non-continuous sense. Additionally, we provide an explicit example to validate our findings. Furthermore, we discuss a general model for fractional differential equations using the Caputo derivative. Finally, we outline the benefits of our study and suggest potential areas for future research.