In this work, we are concerned with a sequential nonlinear random
differential equation of fractional order with nonlocal conditions. This
is the first time in the literature where sequential problems and random
ones are combined and considered. An existence and uniqueness of
solutions for the problem is obtained by means of an appropriate random
fixed point theorem. Then, new concepts on the sequential continuous and
fractional derivative dependence are introduced. At the end, some
results of stability on random, as well for deterministic, data
dependence are discussed.