scholarly journals Geometric Inequalities via a Symmetric Differential Operator Defined by Quantum Calculus in the Open Unit Disk

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Rabha W. Ibrahim ◽  
Rafida M. Elobaid ◽  
Suzan J. Obaiys
Keyword(s):  
Differential Operator ◽  
Differential Equations ◽  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Geometric Inequalities ◽  
Quantum Calculus ◽  
Convolution Operation ◽  
Geometric Representations

The present investigation covenants with the concept of quantum calculus besides the convolution operation to impose a comprehensive symmetric q-differential operator defining new classes of analytic functions. We study the geometric representations with applications. The applications deliberated to indicate the certainty of resolutions of a category of symmetric differential equations type Briot-Bouquet.

scholarly journals Symmetric Conformable Fractional Derivative of Complex Variables

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 363 ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Rafida M. Elobaid ◽  
Suzan J. Obaiys
Keyword(s):  
Differential Operator ◽  
Differential Equations ◽  
Unit Disk ◽  
Analytic Functions ◽  
Differential Operators ◽  
Function Theory ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Symmetric Differential Operators

It is well known that the conformable and the symmetric differential operators have formulas in terms of the first derivative. In this document, we combine the two definitions to get the symmetric conformable derivative operator (SCDO). The purpose of this effort is to provide a study of SCDO connected with the geometric function theory. These differential operators indicate a generalization of well known differential operator including the Sàlàgean differential operator. Our contribution is to impose two classes of symmetric differential operators in the open unit disk and to describe the further development of these operators by introducing convex linear symmetric operators. In addition, by acting these SCDOs on the class of univalent functions, we display a set of sub-classes of analytic functions having geometric representation, such as starlikeness and convexity properties. Investigations in this direction lead to some applications in the univalent function theory of well known formulas, by defining and studying some sub-classes of analytic functions type Janowski function and convolution structures. Moreover, by using the SCDO, we introduce a generalized class of Briot–Bouquet differential equations to introduce, what is called the symmetric conformable Briot–Bouquet differential equations. We shall show that the upper bound of this class is symmetric in the open unit disk.

scholarly journals Generalized Briot-Bouquet Differential Equation Based on New Differential Operator with Complex Connections

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 42 ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Rafida M. Elobaid ◽  
Suzan J. Obaiys
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Linear Operator ◽  
Differential Equations ◽  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk

A class of Briot–Bouquet differential equations is a magnificent part of investigating the geometric behaviors of analytic functions, using the subordination and superordination concepts. In this work, we aim to formulate a new differential operator with complex connections (coefficients) in the open unit disk and generalize a class of Briot–Bouquet differential equations (BBDEs). We study and generalize new classes of analytic functions based on the new differential operator. Consequently, we define a linear operator with applications.

scholarly journals Fractional heat equation optimized by a chaotic function

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 173-178
Author(s):  
Rabha Ibrahim ◽  
Mayada Wazi ◽  
Dumitru Baleanu ◽  
Nadia Al-Saidi
Keyword(s):  
Differential Operator ◽  
Heat Equation ◽  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Fractional Heat Equation ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Extended Operator

In this effort, we propose a new fractional differential operator in the open unit disk. The operator is an extension of the Atangana-Baleanu differential operator without singular kernel. We suggest it for a normalized class of analytic functions in the open unit disk. By employing the extended operator, we study the time-2-D space heat equation and optimizing its solution by a chaotic function.

scholarly journals A New Parametric Differential Operator of p-Valently Analytic Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Samir B. Hadid ◽  
Rabha W. Ibrahim ◽  
G. Murugusundaramoorthy
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Geometric Properties

Newly, numerous investigations are considered utilizing the idea of parametric operators (integral and differential). The objective of this effort is to formulate a new 2D-parameter differential operator (PDO) of a class of multivalent functions in the open unit disk. Consequently, we formulate the suggested operator in some interesting classes of analytic functions to study its geometric properties. The recognized class contains some recent works.

scholarly journals Sandwich Theorems for Multivalent Analytic Functions Associated with Differential Operator

2021 ◽  
Vol 45 (01) ◽  
pp. 7-20
Author(s):  
ABBAS KAREEM WANAS ◽  
ALB LUPAŞ ALINA
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk

The purpose of this paper is to derive subordination and superordination results involving differential operator for multivalent analytic functions in the open unit disk. These results are applied to obtain sandwich results. Our results extend corresponding previously known results.

scholarly journals Study on subclasses of analytic functions

2017 ◽  
Vol 9 (1) ◽  
pp. 122-139 ◽  
Author(s):  
Imran Faisal ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Conjugate Points ◽  
Open Unit ◽  
Open Unit Disk ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Convolution Properties

AbstractBy making use of new linear fractional differential operator, we introduce and study certain subclasses of analytic functions associated with Symmetric Conjugate Points and defined in the open unit disk 𝕌 = {z : |z| < 1}. Inclusion relationships are established and convolution properties of functions in these subclasses are discussed.

scholarly journals Generalized Briot-Bouquet differential equation based on new differential operator with complex connections

2020 ◽  
Vol 28 (1) ◽  
pp. 105-114
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Difference Operator ◽  
Open Unit ◽  
Open Unit Disk ◽  
New Class ◽  
Generalized Operator ◽  
Generalized Differential

AbstractInequality study is a magnificent field for investigating the geometric behaviors of analytic functions in the open unit disk calling the subordination and superordination. In this work, we aim to formulate a generalized differential-difference operator. We introduce a new class of analytic functions having the generalized operator. Some subordination results are included in the sequel.

scholarly journals On a class of analytic functions associated to a complex domain concerning q-differential-difference operator

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Existence Of Solutions ◽  
Difference Operator ◽  
Open Unit ◽  
Convolution Product ◽  
Open Unit Disk ◽  
Current Investigation ◽  
Quantum Calculus ◽  
New Class

AbstractIn our current investigation, we apply the idea of quantum calculus and the convolution product to amend a generalized Salagean q-differential operator. By considering the new operator and the typical version of the Janowski function, we designate definite new classes of analytic functions in the open unit disk. Significant properties of these modules are considered, and recurrent sharp consequences and geometric illustrations are realized. Applications are considered to find the existence of solutions of a new class of q-Briot–Bouquet differential equations.

scholarly journals Some properties of differential operator associated with generalized hypergeometric functions

2015 ◽  
Vol 46 (1) ◽  
pp. 75-83 ◽  
Author(s):  
Entisar El-yagubi ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Derivative Operator ◽  
Generalized Hypergeometric Functions ◽  
Generalized Derivative

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.

scholarly journals Differential Sandwich Theorems for a Certain Class of Analytic Functions Defined by Differential Operator

2019 ◽  
pp. 209-220
Author(s):  
Abbas Kareem Wanas ◽  
Hala Abbas Mehai
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
First Order ◽  
Differential Subordination And Superordination

In this paper, we establish some applications of first order differential subordination and superordination results involving Hadamard product for a certain class of analytic functions with differential operator defined in the open unit disk. These results are applied to obtain sandwich results.

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