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

Ahmadova A., Mahmudov N., Nieto J. J.

Evolution Equations and Control Theory, vol.11, no.6, pp.1997-2015, 2022 (SCI-Expanded) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 11 Say: 6
  • Nəşr tarixi: 2022
  • Doi nömrəsi: 10.3934/eect.2022008
  • jurnalın adı: Evolution Equations and Control Theory
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.1997-2015
  • Açar sözlər: Fractional stochastic differential equations, semigroup theory, stability, stabilization, stochastic degenerate evolution equations, subordination principle
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

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.