Coefficients estimates for certain classes of analytic functions of complex order

Abstract

In this paper, we introduce and investigate the subclasses $$\mathcal {Q} _{g}^{\zeta }(m,\lambda ,\mu ;\gamma )$$ and $$\mathcal {H}_{g}^{\zeta }(m,\lambda ,\mu ,r;u)$$ of analytic functions of complex order defined by a new differential operator involving binomial series. Furthermore, We obtain coefficients bounds and coefficient estimates involving of the nonhomogeneous Cauchy–Euler differential equation of order r. Several corollaries of the main results are also considered.