  Equations built on fractional derivatives prove to be a powerful tool in the
description of complex systems when the effects of singularity, fractal
supports, and long-range dependence play a role. In this paper, we advocate an
application of the fractional derivative formalism to a fairly general class of
critical phenomena when the organization of the system near the phase
transition point is influenced by a competing nonlocal ordering. Fractional
modifications of the free energy functional at criticality and of the widely
known Ginzburg-Landau equation central to the classical Landau theory of
second-type phase transitions are discussed in some detail. An implication of
the fractional Ginzburg-Landau equation is a renormalization of the transition
temperature owing to the nonlocality present.
