On Rabotnov fractional exponential function for bi-univalent subclasses

Abstract

Considering the interesting results obtained recently by studying Rabotnov function, a new investigation is presented in this paper related to the topic of introducing new classes of bi-univalent functions. Using the normalized Rabotnov function and the concept of subordination, a new class of bi-univalent functions [Formula: see text] is defined and studied regarding coefficient estimates. Bounds of the Taylor–Maclaurin coefficients [Formula: see text] and [Formula: see text] are given and using those estimates, Fekete–Szegö problem is also investigated for the newly introduced class. For particular values of the parameters involved in the definition of the class [Formula: see text], certain particular classes are obtained and investigated in the corollaries associated to each result proved for the class [Formula: see text].