Regularity of mild solutions to fractional Cauchy problems with Riemann-Liouville fractional derivative (Q2926349)

The authors investigate the extension of the fact that a sectorial operator can determine an analytic semigroup. They first show that a sectorial operator can determine a real analytic alpha-order fractional resolvent which is defined in terms of the Mittag-Leffler function and a curve integral. Then they give some properties of real analytic alpha-order fractional resolvent. Finally, based on these properties, they discuss the regularity of mild solution of a class of fractional abstract Cauchy problems with Riemann-Liouville fractional derivative.