In the present investigation, new subclasses of analytic functions in the open unit disk which are defined using generalized derivative operator are introduced. Several interesting properties of these classes are obtained.

We provide a validation of a formal approximate solution to the problem of the evolution of a slowly varying harvested logistic population. Using a contraction mapping proof, we show that the initial value problem for the population has an exact solution lying in an appropriately small neighbourhood of this approximate solution, under quite general conditions.

The aim of this paper is to determine the Fekete-Szegö inequalities for a normalized analytic function defined on the open unit disk lies in a region starlike with respect to 1 and it is symmetric with respect to the real axis by using the operator given recently by the authors. As a special case of this result, Fekete-Szegö inequality for a class of functions defined by fractional derivatives is also obtained.

Using a generalized derivative operator, we introduce and study a new class of harmonic univalent functions. In the present paper, we investigate some results for functions f belong to this class which include the necessary and sufficient coefficient bounds. Growth bounds and a closure property are also obtained.

Motivated by generalized derivative operator defined by the authors (El-Yagubi and Darus, 2013) and the technique of differential subordination, several interesting properties of the operator are given.

The aim of this paper is to introduce a new class of analytic functions in the unit disk, with negative coefficients, via a new generalized derivative operator. We prove coecient inequalities for the new class of functions and for a subclass of it, as well as distortion theorems for functions in this subclass and for their derivatives. We determine the extreme points of the newly introduced subclass.

In the present paper, the coefficient estimate of a class of funtions starlike with respect to k-symmetric points defined by generalised derivative operator will be studied. The integral representation and several coefficient inequalities of functions belonging to this class will be given.

This work considers a harvested logistic population for which birth rate, carrying capacity and harvesting rate all vary slowly with time. Asymptotic results from earlier work, obtained using a multiscaling technique, are combined to construct approximate expressions for the evolving population for the situation where the population initially survives to a slowly varying limiting state, but then, due to increasing harvesting, is reduced to extinction in finite time. These results are shown to give very good agreement with those obtained from numerical computation.

In the present paper, two new subclasses of analytic functions with respect to k-symmetric points defined by differential operator. Some interesting properties belonging to these classes are provided.

A new generalised derivative operator is introduced. This operator generalised many well-known operators studied earlier by many authors. New subclasses of analytic functions in the open unit disc are introduced which are defined using generalized derivative operator. Inclusion theorems are investigated for functions to be in the classes. Furthermore, generalised Bernardi-Libera-Livington integral operator is shown to be preserved for these classes.