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Mild solutions for fractional differential equations with nonlocal conditions. (English) Zbl 1192.34010

Summary: This paper is concerned with the existence and uniqueness of a mild solution of the fractional differential equations with nonlocal conditions
\[ d^qx(t)/dt^q=-Ax(t)+f(t,x(t),\quad Gx(t)),\;t\in [0,T], \]
and
\[ x(0)+g(x)=x_0, \]
in a Banach space \(X\), where \(0<q<1\). General existence and uniqueness theorem, which extend many previous results, are given.

MSC:

34A08 Fractional ordinary differential equations
34G20 Nonlinear differential equations in abstract spaces
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References:

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