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In this paper, we study the exact asymptotic separation rate of two distinctsolutions of Caputo stochastic multi-term differential equations (Caputo SMTDEsfor short). Our goal in this paper is to establish results on the globalexistence and uniqueness and continuity dependence of the initial values of thesolutions to Caputo SMTDEs with non-permutable matrices of order $\alpha \in(\frac{1}{2},1)$ and $\beta \in (0,1)$ whose coefficients satisfy a standardLipschitz condition. For this class of systems, we then show the asymptoticseparation property between two different solutions of Caputo SMTDEs with amore general condition based on $\lambda$. Also, the asymptotic separation ratefor the two distinct mild solutions reveals that our asymptotic results aregeneral.

Asymptotic behavior of solutions to fractional stochastic multi-term differential equation systems involving non-permutable matrices