On the some subclasses of bi-univalent functions related to the Faber polynomial expansions and the Fibonacci numbers

Abstract

In this investigation, by using the Tremblay fractional derivative operator, we introduce the new class J^μ,ρ<inf>Σ,γ</inf>(p) of bi-univalent functions based on the rule of subordination. Moreover, we use the Faber polynomial expansions and Fibonacci numbers to derive bounds for the general coefficient |a<inf>n</inf>| of the bi-univalent function class.