ON NONAUTONOMOUS EVOLUTION EQUATIONS WITH A TIME-FRACTIONAL ATTENUATION

Abstract

We consider the maximal regularity problem for parabolic and hyperbolic nonautonomous evolution equations in Hilbert space damped by some nonlocal time-fractional derivative with time-dependent variable-order. We prove the existence, uniqueness and other regularity properties of the solutions of these problems under minimal regularity assumptions on the operators, initial data and inhomogeneous terms.