This paper is concerned with the problem of stochastic stability analysis for fractional-order Markovian jumping complex-valued neural networks (MJCVNNs) with time-varying delays. The novelty of this study is emphasized in two phases. In first phase, MJCVNNs is considered in the form of fractional-order systems. Secondly, complex-valued Wirtinger based integral inequality is newly constructed. The existence and uniqueness conditions of the proposed systems are derived based on the homeomorphism theorem in the complex domain. Then, the stochastic stability condition is derived in terms of linear matrix inequalities (LMIs) for the MJCVNNs by employing Lyapunov indirect method. The feasibility of the derived conditions is verified by the numerical examples and their simulation results are demonstrated to show the effectiveness of the fractional-order derivatives and proposed approach.

本文涉及具有时变时滞的分数阶马尔可夫跳跃复值神经网络（MJCVNNs）的随机稳定性分析问题。该研究的新颖性分两个阶段进行。在第一阶段，MJCVNN以分数阶系统的形式被考虑。其次，重新构造了基于维特林格的积分不等式。基于复域中的同胚定理，推导了所提出系统的存在性和唯一性条件。然后，采用Lyapunov间接方法，根据MJCVNN的线性矩阵不等式（LMI）推导了随机稳定性条件。