Coefficient Estimates for Certain Subclasses of Analytic Functions Defined by New Differential Operator

The study of operators plays an essential role in Mathematics, especially in Geometric Function Theory in Complex Analysis and its related fields. Many derivative and integral operators can be written in terms of convolution of certain analytic functions. The class of analytic functions, which has an essential place in the theory of geometric functions, has been studied by many researchers before. This topic still maintains its popularity today. In this paper, we investigate certain subclasses of analytic functions defined by generalized differential operators involving binomial series. Also, we obtain coefficient estimates involving of the nonhomogeneous Cauchy-Euler differential equation of order r.