Analytical study of existence, uniqueness, and stability in impulsive neutral fractional Volterra-Fredholm equations

Volume 38, Issue 3, pp 313--329 https://dx.doi.org/10.22436/jmcs.038.03.03

Publication Date: December 16, 2024 Submission Date: March 21, 2024 Revision Date: April 13, 2024 Accteptance Date: July 25, 2024

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Authors

P. Raghavendran - Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R\(\&\)D Institute of Science and Technology, Chennai-600062, Tamil Nadu, India. 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), Kalyani, Jodhpur 342030, India. Sh. S. Santra - Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal 741235, India. Dumitru Baleanu - Department of Computer Science and Mathematics, Lebanese American University, Beirut-11022801, Lebanon. - Instiute of Space Sciences-Subsidiary of INFLPR, Magurele-Bucharest, 077125 Magurele, Romania. D. Majumder - Department of Mathematics, JIS College of Engineering, Kalyani, Kalyani, West Bengal 741235, India.

Abstract

This investigation focuses on an impulsive Volterra-Fredholm integro-differential equation enriched with fractional Caputo derivatives and subject to specific order conditions. The study establishes both the existence and uniqueness of analytical solutions using the Banach principle. Moreover, it reveals a distinctive outcome regarding the existence of at least one solution, supported by conditions derived from the Krasnoselskii fixed point theorem. Additionally, the paper extends its examination to impulsive neutral Volterra-Fredholm integro-differential equations, providing insights into their long-term behavior through Ulam stability. The inclusion of an illustrative example emphasizes the practical significance and reliability of the results.

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Keywords

• Caputo fractional derivative
• Volterra-Fredholm integro-differential equation (IDE)
• Arzela-Ascoli theorem
• Banach contraction principle
• Krasnoselskii fixed point theorem
• Ulam stability

MSC

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

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