Ya-Ning Li, Hong-Rui Sun
Abstract:
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.
Submitted November 29, 2013. Published August 29, 2014.
Math Subject Classifications: 34G10.
Key Words: Fractional drivative; Cauchy problem; Mittag-Leffler function;
mild solution.
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Ya-Ning Li School of Mathematics and Statistics Lanzhou University Lanzhou, Gansu 730000, China email: liyn08@lzu.edu.cn | |
Hong-Rui Sun School of Mathematics and Statistics Lanzhou University Lanzhou, Gansu 730000, China email: hrsun@lzu.edu.cn |
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