标题： 分数系统局部稳定流形定理的再探讨 显示英文标题

标题： Local Stable Manifold theorem for fractional systems revisited

摘要： 分数阶微积分的主题在过去几十年中经历了迅速的发展。 特别是分数阶微分方程领域受到了广泛关注。 已经获得了一些理论结果，并开发了强大的数值方法。 尽管在分数阶动力系统领域进行了大量数值模拟，但获得的解析结果却非常少。 为此，本文作者已将局部稳定流形定理扩展到分数阶系统\cite{deshpande2016local}的情况。 Cong 等人\cite{cong2016stable}指出，在具有矩阵参数的双参数 Mittag-Leffler 函数的渐近展开中存在差异（文章\cite{deshpande2016local}中的\textit{参见}引理 4 第 2 部分）。 在本次交流中，我们给出了相同的修正展开式，并通过遵循\cite{deshpande2016local}中给出的相同方法证明了局部稳定流形定理。 显示英文摘要

摘要： The subject of fractional calculus has witnessed rapid development over past few decades. In particular the area of fractional differential equations has received considerable attention. Several theoretical results have been obtained and powerful numerical methods have been developed. In spite of the extensive numerical simulations that have been carried out in the area of fractional order dynamical systems, analytical results obtained are very few. In pursuance to this, present authors have extended local stable manifold theorem in case of fractional systems \cite{deshpande2016local}. Cong et al. \cite{cong2016stable} have pointed out discrepancies in the asymptotic expansion of two-parameter Mittag-Leffler functions with matrix argument (\textit{cf.} Lemma 4 part 2 of article \cite{deshpande2016local}). In the present communication we give the corrected expansion of the same and prove the local stable manifold theorem by following the same approach given in \cite{deshpande2016local}.