Journal of Prime Research in Mathematics

# $$λ$$-fractional schwarzian derivative and $$λ$$-fractional mobius transformation

Y. Polatoglu
Department of Mathematics and Computer Science, Istanbul Kultur University, Bakırkoy 34156, Istanbul, Turkey.

$$^{1}$$Corresponding Author: y.polatoglu@iku.edu.tr

### Abstract

We denote by A the class of all analytic functions in the open unit disk $$\mathbb{D} = {z | |z| < 1}$$ which satisfy the conditions $$f(0) = 0$$, $$f'(0) = 1$$. In this paper we define a new concept of $$λ$$− fractional Schwarzian derivative and $$λ$$− fractional Mobius transformation for the class A. We also formulate the criterion for a function to be univalent using the fractional Schwarzian.

#### Keywords:

$$λ$$-fractional integral, $$λ$$-fractional derivative.