Generalized classes of starlike and convex functions of order α

Abstract

We have introduced, in this paper, the generalized classes of starlike and convex functions of order α by using the fractional calculus. We then proved some subordination theorems, argument theorems, and various results of modified Hadamard product for functions belonging to these classes. We have also established some properties about the generalized Libera operator defined on these classes of functions.

Keywords

• subordination
• fractional derivative
• fractional integral
• generalized Libera operator.