Electron. J. Diff. Equ.,
Vol. 2014 (2014), No. 184, pp. 113.
Regularity of mild solutions to fractional Cauchy problems
with RiemannLiouville fractional derivative
YaNing Li, HongRui 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 alphaorder fractional resolvent which
is defined in terms of MittagLeffler function and the curve integral.
Then we give some properties of real analytic alphaorder fractional
resolvent. Finally, based on these properties, we discuss the regularity
of mild solution of a class of fractional abstract Cauchy problems
with RiemannLiouville fractional derivative.
Submitted November 29, 2013. Published August 29, 2014.
Math Subject Classifications: 34G10.
Key Words: Fractional drivative; Cauchy problem; MittagLeffler function;
mild solution.
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YaNing Li
School of Mathematics and Statistics
Lanzhou University
Lanzhou, Gansu 730000, China
email: liyn08@lzu.edu.cn


HongRui Sun
School of Mathematics and Statistics
Lanzhou University
Lanzhou, Gansu 730000, China
email: hrsun@lzu.edu.cn

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