Let S ∗ λ (1−b)(b 6= 0, complex) denote the class of functions f(z) = z+a2z 2+· · · analytic in the open unit disc D = {z ∈ C

z| < 1} which satisfy for z = reiθ ∈ D, f(z) z 6= 0 and Re · 1 + 1 b µ z (Dλ f(z))′ D λ f(z) − 1 ¶¸ > 0 (0 ≤ λ < 1), where Dλ f(z) = Γ(2 − λ)z λD λ z f(z) and Dλ z f(z) is the fractional derivative of f(z). The aim of this paper is to investigate certain properties of the mentioned above class.