Local stable manifold of langevin differential equations with two fractional derivatives
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Wang, JinRong; Peng, Shan; O’Regan, D (2017). Local stable manifold of langevin differential equations with two fractional derivatives. Advances in Difference Equations ,
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.