  We introduce complex order fractional derivatives in models that describe
viscoelastic materials. This can not be carried out unrestrictedly, and
therefore we derive, for the first time, real valued compatibility constraints,
as well as physical constraints that lead to acceptable models. As a result, we
introduce a new form of complex order fractional derivative. Also, we consider
a fractional differential equation with complex derivatives, and study its
solvability. Results obtained for stress relaxation and creep are illustrated
by several numerical examples.
