In this paper, we investigate the averaging principle for Caputo-type fractional stochastic differential equations driven by Brownian motion. Different from the approach of integration by parts or decomposing integral interval to deal with the estimation of integral involving singular kernel in the existing literature, we show the desired averaging principle in the sense of mean square by using Hölder inequality via growth conditions on the nonlinear stochastic term. Finally, a simulation example is given to verify the theoretical results.

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In this paper, we study the stability of solutions to conformable stochastic differential equations. Firstly, we show the trivial solution are stochastially stable, stochastically asymptotically stable and almost surely exponentially stable, respectively. Secondly, we show the nontrivial solution are Ulam's type stable in the sense of probabilities. Finally, two examples are given to present the theoretically results.

Summary This article investigates the finite‐time consensus control for stochastic multi‐agent systems (SMASs) by using adaptive techniques. First, we propose a finite‐time adaptive consensus protocol for SMASs with node‐based adaptive law design method. Second, a finite‐time adaptive consensus protocol is also proposed for SMASs by adding a dynamical scaling parameter to the weights on the edges of the communication graph. Finally, two simulation examples are provided to verify the effectiveness of the two consensus protocols.

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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.