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Zbl 1179.34002
Mophou, Gisele M.; N'Guerekata, Gaston M.
Mild solutions for semilinear fractional differential equations.
(English)
[J] Electron. J. Differ. Equ. 2009, Paper No. 21, 9 p., electronic only (2009). ISSN 1072-6691/e

The authors study the fractional semilinear differential equation with nonlocal conditions $$D^{q}x(t)=-Ax(t)+f(t,x(t),Bx(t)),\qquad t\in [0,T],$$ $$x(0)+g(x)=x_0,$$ where $T>0,$ $0<q<1,$ $-A$ generates an analytic compact semigroup $(S(t))_{t\ge0}$ of uniformly bounded linear operators on a Banach space $X$. \par By using the Krasnoselkii and the contraction mapping principle, the existence and uniqueness of a mild solution for a fractional semilinear differential equation with non local conditions are given.
[Chuanzhi Bai (Huaian)]
MSC 2000:
*34A08
26A33 Fractional derivatives and integrals (real functions)
34G20 Nonlinear ODE in abstract spaces

Keywords: fractional differential equation; mild solution

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