Results on approximate controllability of neutral integro‐differential stochastic system with state‐dependent delay

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Abstract

This article is mainly focusing on the approximate controllability of neutral integro‐differential stochastic equations with state‐dependent delay. The main results of this article are proved by applying some ideas about the semigroup theory and resolvent operators. At first, the investigation about the existence of a mild solution and then we discuss the approximate controllability of the considered system. Next, we extend our study to the system with non‐local conditions. Finally, a theoretical application is presented for proving the validity of controllability results obtained.

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Most cited references 41

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Is Open Access

On a mild solution of a semilinear functional-differential evolution nonlocal problem

Ludwik Byszewski, Haydar Akca (1997)

The existence, uniqueness, and continuous dependence of a mild solution of a nonlocal Cauchy problem for a semilinear functional-differential evolution equation in a general Banach space are studied. Methods of a $C_0 $ semigroup of operators and the Banach contraction theorem are applied. The result obtained herein is a generalization and continuation of those reported in references [2-8].