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

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

This study presents two novel frameworks, termed a quasi-modular <i>b</i>-metric space and a non-Archimedean quasi-modular <i>b</i>-metric space, and various topological properties are provided. Using comparison and simulation functions, this paper rigorously proves several f...

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Bibliographic Details
Main Authors: Ekber Girgin, Abdurrahman Büyükkaya, Neslihan Kaplan Kuru, Mudasir Younis, Mahpeyker Öztürk
Format: Article
Language:English
Published: MDPI AG 2024-09-01
Series:Fractal and Fractional
Subjects:
fixed point
quasi-modular b-metric space
Ulam–Hyers stability
fractional differential equation
Online Access:https://www.mdpi.com/2504-3110/8/10/558
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Summary:This study presents two novel frameworks, termed a quasi-modular <i>b</i>-metric space and a non-Archimedean quasi-modular <i>b</i>-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 <i>b</i>-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.
ISSN:2504-3110

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