Analytical study of existence, uniqueness, and stability in impulsive neutral fractional Volterra-Fredholm equations
Prabakaran Raghavendran, Th. Gunasekar, Shyam Sundar Santra, Dumitru Bǎleanu, D. Dutta Majumder
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.