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.
Highlights
The memory effect of the system must be accounted for in numerous disciplines, such as nuclear reactor dynamics and thermoelasticity
Integro-differential systems have been widely employed in viscoelastic mechanics, fluid dynamics, thermoelastic contact, control theory, heat conduction, industrial mathematics, financial mathematics, biological models, and other domains, one can refer to [1–7]
Very recently in [4], the author presented the controllability of integro-differential inclusions via resolvent operators by employing the facts connected with resolvent operators and Bohnenblust–Karlin’s fixed point
Summary
The memory effect of the system must be accounted for in numerous disciplines, such as nuclear reactor dynamics and thermoelasticity. Very recently in [2], the authors proved the existence and controllability results for the integro-differential frameworks by applying resolvent operator theories and various fixed point theorems. Let us consider the following nonlinear differential evolution equations with control:. We demonstrate the approximate controllability of integro-differential systems using B = I in Sect. Definition 2.3 A continuous function z : [0, c] → X is said to be a mild solution for system (1.1)–(1.2) if z(0) = z0, z (0) = z1, and. Proof Assume that w(t) is the mild solution of system (3.1)–(3.2), along with the control u. For proving the primary task of this section, that is, the approximate controllability of system (4.3)–(4.4), we have to introduce the following hypotheses:. The approximate controllability of system (4.1)–(4.2) implies that of the semilinear control system (1.1)–(1.2)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
