On the Fixed Point Theorem for Large Contraction Mappings with Applications to Delay Fractional Differential Equations

Mesmouli M. B., Akın E., Iambor L. F., Tunç O., Hassan T. S.

Fractal and Fractional, cilt.8, sa.12, 2024 (SCI-Expanded, Scopus) identifier

  • 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.