Null Controllability of Nonlinear Mixed Integro-differential Systems
Celestin A. Nse *
Department of Mathematics, Federal University of Technology Owerri, Imo State, Nigeria.
Faket K. Nama
Department of Mathematics, Federal Polytechnic of Oil and Gas, Bonny, Rivers State, Nigeria.
Richard Oguara
Department of Mathematics, Federal University of Technology, Owerri, Imo State , Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The present paper investigates the existence of mild solutions and provides sufficient conditions for the null controllability of nonlinear mixed integrodifferential systems with unbounded linear operators in Banach spaces. It is observed that, if the linear system is controllable, then the nonlinear equivalence is also controllable by subjecting certain smooth conditions on the perturbation function. The results are obtained using semi group of linear operators, fractional powers of operators and the Schauder fixed point theorem.
Keywords: Unbounded operators, infinite delays, compactness