Some statistical properties was studied for discret maps obtained from kicked differential equations of motion with derivatives of noninteger orders, more specifically, for a generalization of the standard map considering Caputo fractional derivatives. Thus, the Caputo fractional standard map, parameterized by $K$ and $1<\alpha\leq2$, is derived from Caputo Generalization nonlinear Volterra integral equations of second kind. The survival probability that a particle moving along phase space has to survive a specific domain has a short plateau follow by a decay exponential and present a interesting property, it is scaling invariant for all control parameters.