On a new class of analytic functions related to fractional calculus

Abstract

Let A be the class of analytic functions f with f(0) = 0 and f'(0) = 1 in the open unit disk U. Applying the fractional derivative D-z(lambda) f of order lambda for f is an element of A, a new subclass A(alpha, beta; lambda) of A with 0 <= alpha < 1, beta > 1 and 0 <= lambda < 1 is considered. The object of the present paper is to discuss some interesting properties of this class of functions.