具有离散时滞的Caputo分数阶微分方程的稳定性
Stability of Caputo Fractional DifferentialEquations with Discrete Delay
摘要: 本文利用不动点定理，建立了无限时间离散分布时滞分数阶随机微分方程，主要研究无限时间区间内具有布朗运动和离散分布时滞的Caputo分数阶微分方程解的存在性、唯一性和渐近稳定性。其中，运用压缩映射原理和Mittag-Lefer函数的精准估计。最终，运用反证法证明出了渐近稳定性。
Abstract:
In this paper, we establish infinite time discrete fractional stochastic differential equations with distributed delays by using the fixed point theorem. We mainly study the existence, uniqueness and asymptotic stability of solutions of Caputo fractional differential equations with Brownian motion and discrete distributed delays in infinite time intervals. Among them, the compression mapping principle and accurate estimation of Mittag Leffler function are used. Finally, the asymptotic stability is proved by the method of contradiction.
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