Results on approximate controllability of Sobolev type fractional stochastic evolution hemivariational inequalities

2020 ◽  
Author(s):  
V. Vijayakumar ◽  
R. Udhayakumar ◽  
Sumati Kumari Panda ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Approximate Controllability ◽  
Hemivariational Inequalities ◽  
Sobolev Type ◽  
Stochastic Evolution ◽  
Evolution Hemivariational Inequalities

scholarly journals Optimal Control of Second Order Stochastic Evolution Hemivariational Inequalities with Poisson Jumps

2017 ◽  
Vol 21 (6) ◽  
pp. 1455-1475 ◽  
Author(s):  
Palanisamy Muthukumar ◽  
Nagarajan Durga ◽  
Fathalla A. Rihan ◽  
Chinnathambi Rajivganthi
Keyword(s):  
Optimal Control ◽  
Second Order ◽  
Hemivariational Inequalities ◽  
Stochastic Evolution ◽  
Poisson Jumps ◽  
Evolution Hemivariational Inequalities

scholarly journals Existence and approximate controllability of Sobolev type fractional stochastic evolution equations

2014 ◽  
Vol 62 (2) ◽  
pp. 205-215 ◽  
Author(s):  
N.I. Mahmudov
Keyword(s):  
Linear System ◽  
Hilbert Spaces ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Sobolev Type ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Approximately Controllable

Abstract We study the existence of mild solutions and the approximate controllability concept for Sobolev type fractional semilinear stochastic evolution equations in Hilbert spaces. We prove existence of a mild solution and give sufficient conditions for the approximate controllability. In particular, we prove that the fractional linear stochastic system is approximately controllable in [0, b] if and only if the corresponding deterministic fractional linear system is approximately controllable in every [s, b], 0 ≤ s < b. An example is provided to illustrate the application of the obtained results.

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