Electron. J. Diff. Equ., Vol. 2014 (2014), No. 184, pp. 1-13.

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

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.

Show me the PDF file (245 KB), TEX file, and other files for this article.

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

Return to the EJDE web page