An application of a certain fractional derivative operator (Q1812989)

The object of the present paper is to introduce and study a linear operator \(N_{0,z}^{\alpha,\beta,\eta}\) which is defined in terms of a certain fractional derivative operator. Various interesting properties of the operator \(N_{0,z}^{\alpha,\beta,\eta}\), including its connection with the Carlson-Shaffer operator L(a,c), are given. It is also shown how these operators can be applied successfully with a view to proving a number of inclusion and connection theorems involving starlike, convex, and prestarlike functions in the open unit disk U.