Work

Study on existence and stability analysis for implicit neutral fractional differential equations of ABC derivative

Year: 2025

Type: article

Abstract: In this paper, we study the existence, uniqueness, and stability analysis of non-linear implicit neutral fractional differential equations involving the Atangana–Baleanu derivative in the Caputo sense. The Banach contraction principle theorem is employed to establish the existence and uniqueness of solutions, while Krasnoselskii’s fixed-point theorem is utilized to further analyze the existence of solutions. Stability analysis is also examined, including results for Ulam–Hyers, generalized Ulam–Hyers, Ulam–Hyers–Rassias, and generalized Ulam–Hyers–Rassias stability. Finally, an example is presented to illustrate the existence and uniqueness of solutions, along with a discussion on their stability.

Source: Partial Differential Equations in Applied Mathematics

DOI: 10.1016/j.padiff.2025.101276

Authors: V. Sowbakiya, R. Nirmalkumar, K. Loganathan, C. Selvamani

Institutions: Ramakrishna Mission Vidyalaya, Manipal University Jaipur, Karpagam Academy of Higher Education

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,470

Funder: Manipal University