CAUCHY PROBLEMS OF NONLINEAR NONAUTONOMOUS FRACTIONAL EVOLUTION EQUATIONS

Abstract

This paper will focus on nonlinear nonautonomous abstract evolution equations with the Riemann–Liouville fractional derivative. The new concepts of classical and mild solutions will be introduced to carry out the study of solvability. Our methods are based on analytic semigroup theory, the probability density function, the fixed point technique and the compactness technique. The main results can be applied to the time variable fractional diffusion equations.