Analysis of Caputo-Type Non-Linear Fractional Differential Equations and Their Ulam–Hyers Stability

Girgin E., Büyükkaya A., Kuru N. K., Younis M., Öztürk M.

Fractal and Fractional, cilt.8, sa.10, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 8 Sayı: 10
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3390/fractalfract8100558
  • Dergi Adı: Fractal and Fractional
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, Directory of Open Access Journals
  • Anahtar Kelimeler: fixed point, fractional differential equation, quasi-modular b-metric space, Ulam–Hyers stability
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

This study presents two novel frameworks, termed a quasi-modular b-metric space and a non-Archimedean quasi-modular b-metric space, and various topological properties are provided. Using comparison and simulation functions, this paper rigorously proves several fixed point theorems in the non-Archimedean quasi-modular b-metric space. As a useful application, it also establishes Ulam–Hyers stability for the fixed point problem. Finally, this study concludes with a unique solution to a non-linear fractional differential equation, making a substantial contribution to the discipline.