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