Let Aα be the class of functions f(z) = z
α
(z + a2z
2 + · · ·)
which are analytic in the open unit disc U. For f(z) ∈ Aα using the fractional
calculus, a subclass S
∗
α
(1−b) which is the class of starlike functions of complex
order (1−b) is introduced. The object of the present paper is to discuss some
properties for f(z) belonging to the class S
∗
α
(1 − b).
2000 Mathematics Subject Classification: 30C45
