分数阶神经网络的s-渐近ω-周期解

S-asymptotically ω-periodic Solution for Fractional-order Neural Networks

文章讨论分数阶神经网络s-渐近ω-周期解的存在唯一性问题,其中分数阶阶数α∈(0,1).运用Mit?tag-Leffler函数给出解的表达形式,并得到有关Mittag-Leffler函数性质的重要引理.利用该引理和Banach压缩映射原理,给出分数阶神经网络s-渐近ω-周期解的存在唯一性证明.

In this paper,we discuss the existence of s-asymptoticallyω-periodic solution for fractional neu?ral networks of order 0<α<1.We give the expression of solution in terms of Mittag-Leffler functions and obtain an important lemma about the properties of Mittag-Leffler functions.By using this lemma and Banach contraction mapping principle,we prove the existence and uniqueness of s-asymptoticallyω-periodic solu?tion to fractional-order neural networks.