Abstract
The approximate controllability of semilinear neutral stochastic integrodifferential inclusions with infinite delay in an abstract space is studied. Sufficient conditions are established for the approximate controllability. The results are obtained by using the theory of analytic resolvent operator, the fractional power theory, and the theorem of nonlinear alternative for Kakutani maps. Finally, an example is provided to illustrate the theory.
Highlights
Controllability is an important concept which plays a vital role in many areas of applied mathematics
Most of the controllability results for nonlinear systems concern the so-called semilinear control systems that consist of a linear part and a nonlinear part
Balasubramaniam and Ntouyas [14] have studied the controllability of the following neutral stochastic functional differential inclusions with infinite delay in abstract space: d [x (t) − f (t, xt)] ∈ [Ax (t) + Bu (t)] dt
Summary
Controllability is an important concept which plays a vital role in many areas of applied mathematics. They studied the problem by applying the theory of fractional power operators and α-norm They supposed that the operator (−A, D(−A)) generates a compact analytic semigroup on H and the corresponding linear system of (2) is approximately controllable. Motivated by [14, 18], we will show the approximate controllability of the following semilinear neutral stochastic integrodifferential inclusions with infinite delay in a Hilbert space:. We suppose that there exists a semigroup which generated by (−A, D(−A)) is compact analytic on H so that the resolvent W(t) is analytic We restrict this integrodifferential inclusion in the Hα and demonstrate the existence of mild solutions by applying ‖⋅‖α and the fractional power theory and prove the approximate controllability for (3) in space H.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
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 call
