Nonlocal-in-time evolution equations

In this talk, we present some classes of nonlocal-in-time evolution equations. In the first part, we treat abstract integrodifferential equations in interpolation scales of Banach spaces and show a well-posedness result for them. As an application, we obtain the local well-posedness for a model describing a viscoelastic fluid with memory. In the second part, we use fractional-in-time diffusion equations to illustrate how the qualitative analysis of solutions can change for specific nonlocal-in-time evolution equations.