Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator

Abstract

In this article, we introduce a general family of analytic and bi-univalent functions in the open unit disk, which is defined by applying the principle of differential subordination between analytic functions and the Tremblay fractional derivative operator. The upper bounds for the general coefficients | a n | of functions in this subclass are found by using the Faber polynomial expansion. We have thereby generalized and improved some of the previously published results.

Keywords

• analytic functions
• univalent functions
• bi-univalent functions
• coefficient estimates
• taylor-maclaurin coefficients
• faber polynomial expansion
• differential subordination
• tremblay fractional derivative operator