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

Autor:	Ekber Girgin, Abdurrahman Büyükkaya, Neslihan Kaplan Kuru, Mudasir Younis, Mahpeyker Öztürk
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	fixed point quasi-modular b-metric space Ulam–Hyers stability fractional differential equation Thermodynamics QC310.15-319 Mathematics QA1-939 Analysis QA299.6-433
Zdroj:	Fractal and Fractional, Vol 8, Iss 10, p 558 (2024)
Druh dokumentu:	article
ISSN:	2504-3110
DOI:	10.3390/fractalfract8100558
Popis:	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.
Databáze:	Directory of Open Access Journals
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