Approximate Controllability of Semilinear Stochastic Integrodifferential System with Nonlocal Conditions

Annamalai Anguraj,K Ramkumar

doi:10.3390/fractalfract2040029

Annamalai Anguraj, K Ramkumar

Open Access

https://doi.org/10.3390/fractalfract2040029

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Abstract

The objective of this paper is to analyze the approximate controllability of a semilinear stochastic integrodifferential system with nonlocal conditions in Hilbert spaces. The nonlocal initial condition is a generalization of the classical initial condition and is motivated by physical phenomena. The results are obtained by using Sadovskii’s fixed point theorem. At the end, an example is given to show the effectiveness of the result.

Highlights

Controllability is one of the essential concepts in mathematical control theory and plays a crucial role in each deterministic and stochastic control system
From our simplest data, there are no results on the approximate controllability of semilinear stochastic integrodifferential systems with nonlocal conditions using Sadovskii’s fixed point theorem within the literature
We study the approximate controllability of a semilinear stochastic integrodifferential system with nonlocal conditions in Hilbert spaces

Summary

Introduction

Controllability is one of the essential concepts in mathematical control theory and plays a crucial role in each deterministic and stochastic control system. Kalman [1] introduced the idea of the controllability for finite-dimensional deterministic linear control systems. In [5,6,7,8,9], Mahmudov et al established results for the controllability of linear and semilinear stochastic systems in Hilbert space. Only a few authors have investigated the controllability of neutral functional integrodifferential systems in Banach spaces by using semigroup theory. From our simplest data, there are no results on the approximate controllability of semilinear stochastic integrodifferential systems with nonlocal conditions using Sadovskii’s fixed point theorem within the literature. This paper is dedicated to the estimation of the approximate controllability of semilinear stochastic integrodifferential control systems with nonlocal conditions using Sadovskii’s fixed point theorem.

Preliminaries

M2B b2

L02 ds

Example

Conclusions