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Zbl 1166.34320
N'Guérékata, Gaston M.
A Cauchy problem for some fractional abstract differential equation with non local conditions. (English)
[J] Nonlinear Anal., Theory Methods Appl. 70, No. 5, A, 1873-1876 (2009). ISSN 0362-546X

The author discusses the existence and uniqueness of a solution to the Cauchy problem for the fractional differential equation with non local conditions $$D^q x(t)=f(t,x(t)),\quad t\in [0,T],\quad x(0)+g(x)=x_0,$$ where $0<q<1$ in a Banach space. Here, the fractional derivative is in the sense of Caputo.
[Li Changpin (Logan)]

MSC 2000:: *34G20 Nonlinear ODE in abstract spaces
34A12 Initial value problems for ODE
26A33 Fractional derivatives and integrals (real functions)

Keywords: Cauchy problem; fractional abstract differential equation; Caputo derivative

Cited in: Zbl 1204.34010 Zbl 1171.34332

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