Analyzing existence, uniqueness, and stability of neutral fractional Volterra-Fredholm integro-differential equations

Volume 33, Issue 4, pp 390--407 https://dx.doi.org/10.22436/jmcs.033.04.06

Publication Date: January 28, 2024 Submission Date: November 23, 2023 Revision Date: December 10, 2023 Accteptance Date: December 22, 2023

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Authors

Th. Gunasekar - Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R\(\&\)D Institute of Science and Technology, Chennai-600062, Tamil Nadu, India. - School of Artifiial Intelligence and Data Science, Indian Institute of Technology (IIT), Jodhpur 342030, Tamil Nadu, India. P. Raghavendran - Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R\(\&\)D Institute of Science and Technology, Chennai-600062, Tamil Nadu, India. Sh. S. Santra - Department of Mathematics , JIS College of Engineering, Kalyani, West Bengal 741235, India. M. Sajid - Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah 51452, Saudi Arabia.

Abstract

This paper explores the investigation of a Volterra-Fredholm integro-differential equation that incorporates Caputo fractional derivatives and adheres to specific order conditions. The study rigorously establishes both the existence and uniqueness of analytical solutions by applying the Banach principle. Additionally, it presents a unique outcome regarding the existence of at least one solution, supported by exacting conditions derived from the Krasnoselskii fixed point theorem. Furthermore, the paper encompasses neutral Volterra-Fredholm integro-differential equations, thus extending the applicability of the findings. Additionally, the paper explores the concept of Ulam stability for the obtained solutions, providing valuable insights into their long-term behavior. To emphasis the practical significance and reliability of the results, an illustrative example is included, effectively demonstrating the applicability of the theoretical discoveries.

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Keywords

• Volterra-Fredholm integro-differential equation
• Banach contraction principle
• Krasnoselskii fixed point theorem
• Arzela-Ascoli theorem
• Ulam stability

MSC

•  26A33
•  34A12
•  26D10
•  26E50
•  45G10
•  45J05

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