UNSTABLE MANIFOLDS FOR FRACTIONAL DIFFERENTIAL EQUATIONS

Abstract

We prove the existence of unstable manifolds for an abstract semilinear fractional differential equation Dαu(t) = Au(t) + f(u(t)), u(0) = u 0 , on a Banach space. We then develop a general approach to establish a semidiscrete approximation of unstable manifolds. The main assumption of our results are naturally satisfied. In particular, this is true for operators with compact resolvents and can be verified for finite elements as well as finite differences methods.