A New Class of Analytic Normalized Functions Structured by a Fractional Differential Operator

Najla M Alarifi,Rabha W Ibrahim,Sarfraz Nawaz Malik

doi:10.1155/2021/6270711

Abstract

Newly, the field of fractional differential operators has engaged with many other fields in science, technology, and engineering studies. The class of fractional differential and integral operators is considered for a real variable. In this work, we have investigated the most applicable fractional differential operator called the Prabhakar fractional differential operator into a complex domain. We express the operator in observation of a class of normalized analytic functions. We deal with its geometric performance in the open unit disk.

Highlights

The class of complex fractional operators is investigated geometrically by Srivastava et al [1] and generalized into two-dimensional fractional parameters by Ibrahim for a class of analytic functions in the open unit disk [2]
We formulate an arrangement of the fractional differential operator in the open unit disk refining the well-known Prabhakar fractional differential operator
We present a class of analytic functions by

Summary

Introduction

The class of complex fractional operators (differential and integral) is investigated geometrically by Srivastava et al [1] and generalized into two-dimensional fractional parameters by Ibrahim for a class of analytic functions in the open unit disk [2]. These operators are consumed to express different classes of analytic functions, fractional analytic functions [3] and differential equations of a complex variable, which are called fractional algebraic differential equations studding the Ulam stability [4, 5]. We carry on our investigation in the field of complex fractional differential operators. We study the classes in terms of the geometric function theory

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