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:


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.


\(λ\)-fractional integral, \(λ\)-fractional derivative.