Our main goal is the study of fractional evolution equations, under appropriate initial and boundary conditions, posed on a Banach space. Such problems have their origin in different fields of science and engineering, such as linear viscoelasticity, diffusion processes in materials with memory, electrodynamics with memory or in the approximation of non-linear conservation laws. On the one hand, we are interested in analysing under what conditions it can be assured that the problem is well proposed in the sense of Hadamard, the maximal regularity property, etc., and on the other hand, we are interested in studying possible techniques for approximating the solution.

University education