Neighborhoods of Analytic Functions Associated with Fractional Derivative

Abstract

In this paper we define a differential operator and introduce the subclasses F-n,p(q) (lambda, alpha, delta) and K-n,p(q) (lambda, alpha, delta, mu) of functions which are analytic and p-valent in the open unit disk. Also we derive coefficient bounds, distortion inequalities, associated inclusion relation for (n, epsilon)-neighborhoods of the classes, which are defined by means of a certain non-homogeneous differential equation.