Abstract
In this paper, we study the stability of Caputo-type fractional stochastic differential equations. Stochastic stability and stochastic asymptotical stability are shown by stopping time technique. Almost surly exponential stability and pth moment exponentially stability are derived by a new established Itô’s formula of Caputo version. Numerical examples are given to illustrate the main results.
Highlights
Fractional derivative is used to study the properties of memory and genetic for complex systems in different fields of application; see [2, 6]
Wu et al [23] introduced a new result for Mittag-Leffler stability analysis of fractional discrete-time neural networks via fixed point technique
For more details on fractional differential equations, we refer to the monographs [12, 25]
Summary
Fractional derivative is used to study the properties of memory and genetic for complex systems in different fields of application; see [2, 6]. Burton et al [3,4,5] presented the application of fixed point technology to stability analysis and fractional differential equations. Uniqueness and stability of solutions to stochastic partial differential equations have been studied by many researchers; see [2, 8, 15, 17, 20]. Doan et al [8] studied asymptotic separation between solutions of the following Caputo fractional stochastic differential equations: CD0α+ X(t) = f t, X(t). Note that asymptotic behavior and exponential stability of fractional stochastic differential equations in the sense of expected have been studied in [6, 16]. Numerical simulation illustrates our theoretical results in the final section
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