Existence and controllability results for neutral fractional Volterra-Fredholm integro-differential equations

Volume 34, Issue 4, pp 361--380 https://dx.doi.org/10.22436/jmcs.034.04.04

Publication Date: April 05, 2024 Submission Date: December 05, 2023 Revision Date: December 24, 2023 Accteptance Date: February 21, 2024

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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 Artificial Intelligence and Data Science, Indian Institute of Technology (IIT), Jodhpur 342030, 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 delves into the investigation of a Volterra-Fredholm integro-differential equation enhanced with Caputo fractional derivatives subject to specific order conditions. The study rigorously establishes the existence of solutions through the application of the Schauder fixed-point theorem. Furthermore, it encompasses neutral Volterra-Fredholm integro-differential equations, thereby extending the applicability of the findings. In addition, the paper explores the concept of controllability for the obtained solutions, offering valuable insights into how these solutions behave over extended time periods.

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Keywords

• Volterra-Fredholm integro-differential equations
• fractional derivatives
• controllability
• Schauder fixed point theorem

MSC

•  26A33
•  26D10
•  34A12
•  45G10
•  45J05
•  47G20

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