On stable manifolds for fractional differential equations in high dimensional spaces

TL;DR

This paper develops a theoretical framework to establish the existence of stable manifolds near hyperbolic equilibria for fractional differential equations in high-dimensional spaces.

Contribution

It extends the theory of stable manifolds to fractional differential equations in arbitrary finite-dimensional spaces, which was previously less understood.

Findings

Proves the existence of stable manifolds for fractional differential equations.

Provides a method applicable to high-dimensional systems.

Enhances understanding of stability in fractional dynamical systems.

Abstract

Our aim in this paper is to establish stable manifolds near hyperbolic equilibria of fractional differential equations in arbitrary finite dimensional spaces.