On Approximate Controllability of Second Order Fractional Impulsive Stochastic Differential System with Nonlocal, State-dependent Delay and Poisson Jumps

American journal of applied mathematics and statistics Pub Date : 2021-04-26 DOI:10.11648/J.AJAM.20210902.13

K. Thiagu

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引用次数: 2

Abstract

The main scope of this paper is to focus the approximate controllability of second order (q∈(1,2]) fractional impulsive stochastic differential system with nonlocal, state-dependent delay and Poisson umps in Hilbert spaces. The existence of mild solutions is derived by using Schauder fixed point theorem. Sufficient conditions for the approximate controllability are established by under the assumptions that the corresponding linear system is approximately controllable and it is checked by using Lebesgue dominated convergence theorem. The main results are completly based on the results that the existence and approximate controllability of the fractional stochastic system of order 1

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二阶分数阶脉冲随机微分系统非局部、状态相关时滞和泊松跳的近似可控性

本文主要研究了二阶(q∈(1,2])分数阶脉冲随机微分系统在Hilbert空间中的近似可控性，该系统具有非局部、状态相关的时滞和泊松峰。利用Schauder不动点定理，导出了温和解的存在性。在相应的线性系统近似可控的前提下，建立了近似可控的充分条件，并用Lebesgue主导收敛定理对其进行了检验。主要结果完全基于1阶

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American journal of applied mathematics and statistics

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