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A Cauchy problem for some fractional abstract differential equation with non local conditions. (English) Zbl 1166.34320
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.

##### MSC:
 34G20 Nonlinear ODE in abstract spaces 34A12 Initial value problems for ODE, existence, uniqueness, etc. of solutions 26A33 Fractional derivatives and integrals (real functions)
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##### References:
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