Approximate Controllability Results for Second Order Neutral Impulsive Stochastic Evolution Equations of Sobolev Type with Unbounded Delay

2019 ◽  
Vol 8 (2) ◽  
pp. 291-304 ◽  
Author(s):  
R. Nirmalkumar ◽  
R. Murugesu
Keyword(s):  
Approximate Controllability ◽  
Evolution Equations ◽  
Second Order ◽  
Sobolev Type ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Unbounded Delay

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.

Approximate controllability and existence of mild solutions for Riemann-Liouville fractional stochastic evolution equations with nonlocal conditions of order 1 < α < 2

2019 ◽  
Vol 22 (4) ◽  
pp. 1086-1112 ◽  
Author(s):  
Linxin Shu ◽  
Xiao-Bao Shu ◽  
Jianzhong Mao
Keyword(s):  
Approximate Controllability ◽  
Stochastic Systems ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Mönch Fixed Point Theorem ◽  
Liouville Derivative ◽  
Liouville Fractional Derivative

Abstract In this paper, we consider the existence of mild solutions and approximate controllability for Riemann-Liouville fractional stochastic evolution equations with nonlocal conditions of order 1 < α < 2. As far as we know, there are few articles investigating on this issue. Firstly, the mild solutions to the equations are proved using Laplace transform of the Riemann-Liouville derivative. Moreover, the estimations of resolve operators involving the Riemann-Liouville fractional derivative of order 1 < α < 2 are given. Then, the existence results are obtained via the noncompact measurement strategy and the Mönch fixed point theorem. The approximate controllability of this nonlinear Riemann-Liouville fractional nonlocal stochastic systems of order 1 < α < 2 is concerned under the assumption that the associated linear system is approximately controllable. Finally, the approximate controllability results are obtained by using Lebesgue dominated convergence theorem.

Sign in / Sign up

Export Citation Format

Share Document