Subordination principle and approximation of fractional resolvents and applications to fractional evolution equations

Abstract

This paper first analyzes and treats the subordination principle and the approximation of fractional resolvents, extending and perfecting the theory of resolvent. Then, the approximation solvability method and the resolvent technique are developed to investigate the existence of mild solutions to a Riemann-Liouville type fractional nonlocal evolution system without the compactness condition. Moreover, effectiveness of our mentioned findings is supported by an example about a fractional diffusion system.