Exponential stability and stabilization of fractional stochastic degenerate evolution equations in a Hilbert space: Subordination principle

Abstract

<p style='text-indent:20px;'>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 nonlinearity. 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.</p>

On Caputo fractional elliptic equation with nonlocal condition

“…The reason they are of interest comes from the model sticking to memory eects. We temporarily list some articles about Caputo or Riemann-Liouville [1,2,3,18,10,12,14,9,11,15,20,13,19] and some other Email address: tiennv55@fe.edu.vn (Van Tien Nguyen) derivatives, see [21, 22? , 23, 24, 25].…”

Fractional evolution equation with Cauchy data in $L^{p}$ spaces

“…Recently, it has been widely used in modeling practical models because of its ability to provide approximation and ignore the influence of external forces such as in physics, engineering, mechanics science, biology, and some other areas [1][2][3][4][5]. There are several versions of noninteger derivatives, but perhaps the two types of derivatives, Caputo and Riemann-Liouville, are of most interest to mathematicians [6][7][8][9][10][11][12][13][14][15].…”