  We investigate the solution to the logistic equation involving non-local
operators in time. In the linear case such operators lead to the well-known
theory of time changes. We provide the probabilistic representation for the
non-linear logistic equation with non-local operators in time. The so-called
fractional logistic equation has been investigated by many researchers, the
problem to find the explicit representation of the solution on the whole real
line is still open. In our recent work the solution on compact sets has been
written in terms of Euler's numbers.
