Approximate controllability of fractional neutral stochastic evolution equations in Hilbert spaces with fractional Brownian motion

2017 ◽  
Vol 36 (2) ◽  
pp. 209-223
Author(s):  
Kerboua Mourad
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Hilbert Spaces ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations

scholarly journals Transportation Inequalities for Coupled Fractional Stochastic Evolution Equations Driven by Fractional Brownian Motion

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Wentao Zhan ◽  
Yuanyuan Jing ◽  
Liping Xu ◽  
Zhi Li
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Hurst Parameter ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Uniform Distance

In this paper, we consider the existence and uniqueness of the mild solution for a class of coupled fractional stochastic evolution equations driven by the fractional Brownian motion with the Hurst parameter H∈1/4,1/2. Our approach is based on Perov’s fixed-point theorem. Furthermore, we establish the transportation inequalities, with respect to the uniform distance, for the law of the mild solution.

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.

scholarly journals Abstract Functional Stochastic Evolution Equations Driven by Fractional Brownian Motion

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Mark A. McKibben ◽  
Micah Webster
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Evolution Equations ◽  
Separable Hilbert Space ◽  
Mild Solutions ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Convergence Results ◽  
Real Separable Hilbert Space ◽  
Wave Phenomena

We investigate a class of abstract functional stochastic evolution equations driven by a fractional Brownian motion in a real separable Hilbert space. Global existence results concerning mild solutions are formulated under various growth and compactness conditions. Continuous dependence estimates and convergence results are also established. Analysis of three stochastic partial differential equations, including a second-order stochastic evolution equation arising in the modeling of wave phenomena and a nonlinear diffusion equation, is provided to illustrate the applicability of the general theory.

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