Equações de evolução fracionárias em escalas de interpolação e aplicações

Abstract

This work is dedicated to the study of linear and semilinear evolution equations with Caputo fractional derivative, and linear part governed by a sectorial operator. In the first case, we study estimates on the families of linear operators associated with the problem in abstract interpolation scales and sufficient conditions to global well-posedness and spatial regularity of mild solutions. In the semilinear situation, we study the existence and uniqueness of local mild solutions to the problem and their possible continuation to a maximal interval of existence. We also study the problem of spatial regularity and continuous dependence with respect to initial data. Finnaly, we study applications of the abstract results to diffusion-wave equations and fractional plate equations.