A note on the approximate controllability of second-order integro-differential evolution control systems via resolvent operators

Abstract

Abstract The approximate controllability of second-order integro-differential evolution control systems using resolvent operators is the focus of this work. We analyze approximate controllability outcomes by referring to fractional theories, resolvent operators, semigroup theory, Gronwall’s inequality, and Lipschitz condition. The article avoids the use of well-known fixed point theorem approaches. We have also included one example of theoretical consequences that has been validated.

Keywords

• Approximate controllability
• Gronwall’s inequality
• Resolvent operators
• Second-order integro-differential systems