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On the existence interval for the initial value problem of a fractional differential equation. (English) Zbl 1247.34005
The authors consider the initial problem for the fractional differential equation (FIVP) $$ \cases D_{0+}^a(x-x_0)(t)=f(t,x(t)), \ \ \ t>0,\\ x(0)=x_0, \endcases $$ where the nonlinearity $f:D=[0,T]\times[x_0-b,x_0+b]\to\mathbb{R}$ is assumed to be continuous, and $T,b>0$ and $x_0$ are fixed real numbers. They compute via a comparison function technique, a new bound for the existence interval of the initial value problem for a fractional differential equation given. They improve in this way the estimate of the existence interval obtained very recently in the literature.

34A08Fractional differential equations
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions