Work

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

Year: 2024

Type: article

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.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract8100558

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

Institutions: Sakarya Uygulamalı Bilimler Üniversitesi, Karadeniz Technical University, Sakarya University

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,069

OpenAlex ID: W4402859008

FWCI: 5.365

Cites: 29

Cited by: 8

Related to: 10