Regularity of mild solutions to fractional Cauchy problems with Riemann-Liouville fractional derivative
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 propert...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2014-08-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/184/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |