Somayeh Fadaei - Department of Mathematics, Payame Noor University, P.O.Box ۱۹۳۹۵-۳۶۹۷, Tehran, Iran
Shahram Najafzadeh - Department of Mathematics, Payame Noor University, P.O.Box ۱۹۳۹۵-۳۶۹۷, Tehran, Iran
Ali Ebadian - Department of Mathematics, Urmia University, Urmia, Iran

In this paper, we introduce a newly defined  subclass \mathcal{S}_{\Sigma}(\vartheta,\gamma,\eta;\varphi) of bi-univalent functions by using the Tremblay differential operator satisfying subordinate conditions in the unit disk. Moreover, we use the Faber polynomial expansion to derive bounds for the Fekete-Szego problem and first two \emph{Taylor-Maclaurin coefficients} |a_۲| and |a_۳| for functions of this class.

Analytic function, Bi-univalent function, Coefficient estimates, Faber polynomial expansion, Tremblay fractional derivative operator