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Fractional resolvents and fractional evolution equations. (English) Zbl 1253.34016
The authors generalize the notion of strongly continuous semigroups to fractional differential equations and define the fractional resolvent. After establishing a few properties of this resolvent, the authors apply the results to a fractional-order abstract evolution equation.
Reviewer: Syed Abbas (Mandi)

MSC:
34A08 Fractional ordinary differential equations and fractional differential inclusions
26A33 Fractional derivatives and integrals
34G10 Linear differential equations in abstract spaces
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