New finite-time stability result for a class of Itô-Doob stochastic fractional order systems

Abstract

In this article, we study the Finite-Time Stability (FTS) of Linear Stochastic Fractional Differential Equations of Itô-Doob Type with Delay (LSFDEIDTwD) for a derivative order ρ∈(0,1). In fact, the (FTS) here consists in studying the stability of the (LSFDEIDTwD) in a finite-time domain [0,T]. To our knowledge, this work represents the first successful attempt to study the (FTS) for the (LSFDEIDTwD), where the fractional order ρ∈(0,1). According to the generalized Gronwall Inequality (GWI) and stochastic calculus theory, the (FTS) of (LSFDEIDTwD) is investigated. We illustrate the main results by two numerical examples.

Keywords

• Gronwall inequality
• Stochastic system