Local stable manifold of Langevin differential equations with two fractional derivatives

Advances in Difference Equations

Shan Peng¹  JinRong Wang¹  D ORegan² 

[1] Department of Mathematics, Guizhou University, Guiyang, P.R. China;School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

关键词: local stable manifolds;    Langevin differential equations;    Mittag-Leffler functions;    26A33;    34A34;    34D35;   

DOI  :  10.1186/s13662-017-1389-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we investigate the existence of local center stable manifolds of Langevin differential equations with two Caputo fractional derivatives in the two-dimensional case. We adopt the idea of the existence of a local center stable manifold by considering a fixed point of a suitable Lyapunov-Perron operator. A local center stable manifold theorem is given after deriving some necessary integral estimates involving well-known Mittag-Leffler functions.

【 授权许可】

CC BY