Work

A Study on the Existence, Uniqueness, and Stability of Fractional Neutral Volterra-Fredholm Integro-Differential Equations with State-Dependent Delay

Year: 2024

Type: article

Abstract: This paper presents an analysis of the existence, uniqueness, and stability of solutions to fractional neutral Volterra-Fredholm integro-differential equations, incorporating Caputo fractional derivatives and semigroup operators with state-dependent delays. By employing Krasnoselskii’s fixed point theorem, conditions under which solutions exist are established. To ensure uniqueness, the Banach Contraction Principle is applied, and the contraction condition is verified. Stability is analyzed using Ulam’s stability concept, emphasizing the resilience of solutions to perturbations and providing insights into their long-term behavior. An example is included, accompanied by graphical analysis that visualizes the solutions and their dynamic properties.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9010020

Authors: Prabakaran Raghavendran, Tharmalingam Gunasekar, Junaid Ahmad, Walid Emam

Institutions: Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Indian Institute of Technology Jodhpur, International Islamic University, Islamabad, King Saud University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,069

Funder: King Saud University