Fractal and Fractional (Sep 2024)

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

  • Ekber Girgin,
  • Abdurrahman Büyükkaya,
  • Neslihan Kaplan Kuru,
  • Mudasir Younis,
  • Mahpeyker Öztürk

DOI
https://doi.org/10.3390/fractalfract8100558
Journal volume & issue
Vol. 8, no. 10
p. 558

Abstract

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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.

Keywords