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Zbl 1229.34004
Hernández, Eduardo; O'Regan, Donal; Balachandran, Krishnan
On recent developments in the theory of abstract differential equations with fractional derivatives. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 10, 3462-3471 (2010). ISSN 0362-546X

From the authors' abstract: This note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives. We show that the existence results in a lot of papers are incorrect since the considered variation of constant formula is not appropriate. In this note, we also consider a different approach to treat a general class of abstract fractional differential equations.
[Li Changpin (Logan)]

MSC 2000:: *34A08
34K30 Functional-differential equations in abstract spaces
34G20 Nonlinear ODE in abstract spaces

Keywords: fractional derivatives; abstract Cauchy problem; operator resolvent; abstract integro-differential equations

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Zentralblatt MATH Berlin [Germany]