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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 differential equations in abstract spaces
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
26A33 Fractional derivatives and integrals
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References:

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