Approximate Controllability of Semilinear Neutral Stochastic Integrodifferential Inclusions with Infinite Delay

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.

Analytic resolvent semilinear integro‐differential systems: Existence and optimal control

“…Balakrishnan 2 investigated control problems with state variables in Banach space using the bounded resolvent approach. Integro‐differential systems are widely used in biological models, financial mathematics, industrial mathematics, heat conduction, control theory, thermoelastic contact, fluid dynamics, and viscoelastic mechanics; one can refer to previous studies 3–25 …”

The Existence, Uniqueness, and Controllability of Neutral Stochastic Delay Partial Differential Equations Driven by Standard Brownian Motion and Fractional Brownian Motion

“…This family of equations has great applications in mathematical, electrical engineering, ecology, and other fields of science. In recent years, NDEs have received more and more attention; see, for example, [6][7][8][9][10][11][12][13][14][15][16] and the reference therein.…”

“…The controllability problem is one of the most attractive and important problems of differential equations because of their great significance and applications in physics, population dynamics, engineering, mathematical biology, and other areas of science. Controllability for stochastic models only containing standard Brownian motion has been investigated very well (see [7,12,16,22]). Recently, controllability for stochastic systems only driven by fBm has gained a lot of attention; we refer to [6,9,11].…”

Approximate controllability of neutral delay integro-differential inclusion of order $ \alpha\in (1, 2) $ with non-instantaneous impulses

“…But also have established an abundance of controllability results related to the differential equation and inclusion [1]- [23]. In continuation to controllability results, further extensions related to integrodifferential equation have been explored in many research articles [27]- [17].…”