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EXPONENTIAL STABILITY AND STABILIZATION OF FRACTIONAL STOCHASTIC DEGENERATE EVOLUTION EQUATIONS IN A HILBERT SPACE: SUBORDINATION PRINCIPLE.

Authors :
AHMADOVA, ARZU
MAHMUDOV, NAZIM I.
NIETO, JUAN J.
Source :
Evolution Equations & Control Theory; Dec2022, Vol. 11 Issue 6, p1997-2015, 19p
Publication Year :
2022

Abstract

In this paper, we obtain a closed-form representation of a mild solution to the fractional stochastic degenerate evolution equation in a Hilbert space using the subordination principle and semigroup theory. We study aforesaid abstract fractional stochastic Cauchy problem with nonlinear state-dependent terms and show that if the Sobolev type resolvent families describing the linear part of the model are exponentially stable, then the whole system retains this property under some Lipschitz continuity assumptions for non-linearity. We also establish conditions for stabilizability and prove that the stochastic nonlinear fractional Cauchy problem is exponentially stabilizable when the stabilizer acts linearly on the control systems. Finally, we provide applications to show the validity of our theory. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
21632472
Volume :
11
Issue :
6
Database :
Complementary Index
Journal :
Evolution Equations & Control Theory
Publication Type :
Academic Journal
Accession number :
160750269
Full Text :
https://doi.org/10.3934/eect.2022008