In this paper, exponential stability of nonlinear fractional order stochastic system with Poisson jumps is studied in finite dimensional space. The existence and uniqueness of solution, stability and exponential stability results are established by using boundedness properties of Mittag–Leffler matrix function, fixed point route and local assumptions on nonlinear terms. A numerical example is given to illustrate the efficiency of the obtained results. Finally, conclusion is drawn.

中文翻译：

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具有泊松跳跃的非线性分数随机系统的指数稳定性

本文在有限维空间中研究了具有泊松跳跃的非线性分数阶随机系统的指数稳定性。利用Mittag-Leffler矩阵函数的有界性质、不动点路径和非线性项的局部假设，建立解的存在唯一性、稳定性和指数稳定性结果。给出了一个数值例子来说明所得结果的有效性。最后得出结论。