  The problem whether a given pair of functions can be used as the kernels of a
generalized fractional derivative and the associated generalized fractional
integral is reduced to the problem of existence of a solution to the Sonine
equation. It is shown for some selected classes of functions that a necessary
condition for a function to be the kernel of a fractional derivative is an
integrable singularity at 0. It is shown that locally integrable completely
monotone functions satisfy the Sonine equation if and only if they are singular
at 0.
