ON FULLY NONLINEAR EQUATIONS WITH FRACTIONAL TIME DERIVATIVE: LOCAL EXISTENCE AND UNIQUENESS, STABLE MANIFOLD

We prove a maximal regularity result for abstract linear evolution autonomous equations with a fractional time derivative in the sense of Caputo. We employ it to show theorem of existence and unique-ness of local solutions for fully nonlinear equations and a theorem of existence of a stable manifold which is analogous to well known results in the case of a derivative of order one. We conclude with some exam-ples and applications to mixed Cauchy-Dirichlet and Cauchy-Neumann problems.