Neighborhoods of a Certain Family of Multivalent Functions Defined by Using a Fractional Derivative Operator

Abstract

Making use of a fractional derivative operator, we introduce and investigate two new classes $K_{j}(p,\lambda ,b,\beta )$ and $L_{j}(p,\lambda ,b,\beta ,\mu )$ of multivalently analytic functions of complex order. In this paper we obtain the coefficient estimates and inclusion relationships involving the $(j,\delta )-$ neighborhood of various subclasses of multivalently analytic functions of complex order.