Recently, the authors introduced two interesting subclasses ^*(α, β, γ) and (α, β, γ) of starlike functions in the open unit disk , and proved various coefficient inequalities and distortion theorems for functions belonging to these subclasses. The object of the present sequel is to apply some of these coefficient inequalities in order to deduce substantially more general distortion theorems involving fractional derivatives and fractional integrals of functions belonging to the classes ^*(α, β, γ) and (α, β, γ). Relevant connections of the results presented here with those of the earlier paper are also indicated.