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, vol.8, no.10, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 10
  • Publication Date: 2024
  • Doi Number: 10.3390/fractalfract8100558
  • Journal Name: Fractal and Fractional
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, Directory of Open Access Journals
  • Keywords: fixed point, fractional differential equation, quasi-modular b-metric space, Ulam–Hyers stability
  • Karadeniz Technical University Affiliated: Yes

Abstract

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.