Faber Polynomial Coefficient Estimates for Bi-univalent Functions Defined by the Tremblay Fractional Derivative Operator

Abstract

Using the Tremblay fractional derivative operator in the complex domain, we introduce and investigate a new class of analytic and bi-univalent functions in the open unit disk. We use the Faber polynomial expansions to obtain upper bounds for the general coefficients of such functions subject to a gap series condition as well as obtaining bounds for their first two coefficients.