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 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 The order of convexity for an integral operator

2016 ◽  
Vol 32 (1) ◽  
pp. 123-129
Author(s):  
VIRGIL PESCAR ◽  
◽  
CONSTANTIN LUCIAN ALDEA ◽  
◽  
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Order Of Convexity

In this paper we consider an integral operator for analytic functions in the open unit disk and we derive the order of convexity for this integral operator, on certain classes of univalent functions.

Estimates on Initial Coefficients of Certain Subclasses of Bi-Univalent Functions Associated with Al-Oboudi Differential Operator

2017 ◽  
Vol 84 (1-2) ◽  
pp. 73
Author(s):  
Amol B. Patil ◽  
Uday H. Naik
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk

In the present investigation we introduce two subclasses Ν<sub>Σ</sub><sup>δ</sup>,<sup>μ</sup> [η, α, λ] and Ν<sub>Σ</sub><sup>δ</sup>,<sup>μ</sup> (η, β, λ) of the function class Σ of bi-univalent functions defined in the open unit disk. These subclasses are defined by using the Al-Oboudi differential operator, which is the generalized Salagean's differential operator. Also we find estimates on initial coeffcients |a<sub>2</sub>| and |a<sub>3</sub>| for the functions in these subclasses and consider some related subclasses in connection with these subclasses.

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 Generalizing Certain Analytic Functions Correlative to the n-th Coefficient of Certain Class of Bi-Univalent Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Hameed Ur Rehman ◽  
Maslina Darus ◽  
Jamal Salah
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Positive Real Part ◽  
Polynomial Expansion ◽  
Open Unit ◽  
Open Unit Disk ◽  
Positive Real ◽  
Faber Polynomial ◽  
Coefficient Problems

In the present paper, the authors implement the two analytic functions with its positive real part in the open unit disk. New types of polynomials are introduced, and by using these polynomials with the Faber polynomial expansion, a formula is structured to solve certain coefficient problems. This formula is applied to a certain class of bi-univalent functions and solve the n -th term of its coefficient problems. In the last section of the article, several well-known classes are also extended to its n -th term.

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 On Sandwich Theorems Results for Certain Univalent Functions Defined by Generalized Operators

2021 ◽  
pp. 2376-2383
Author(s):  
Waggas Galib Atshan ◽  
Aqeel Ahmed Redha Ali
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Differential Subordination And Superordination

In this present paper, we obtain some differential subordination and superordination results, by using generalized operators for certain subclass of analytic functions in the open unit disk. Also, we derive some sandwich results.

Estimates for the Koebe Constant and the Second Coefficient for Some Classes of Univalent Functions

1980 ◽  
Vol 32 (6) ◽  
pp. 1311-1324 ◽  
Author(s):  
D. Bshouty ◽  
W. Hengartner ◽  
G. Schober
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
The Other ◽  
Open Unit ◽  
Open Unit Disk ◽  
Identity Mapping ◽  
The Best Possible Constant

Let S be the set of all normalized univalent analytic functions ƒ(z) = z + a2z2 + … in the open unit disk U. Then ƒ(U) contains the disk . Here is the best possible constant and is referred to as the Koebe constant for S. On the other extreme, ƒ(U) cannot contain the disk {|w| < 1}; unless ƒ is the identity mapping.In order to interpolate between the class S and the identity mapping, one may introduce the families , of functions ƒ ∈ S such that ƒ(U) contains the disk {|w| < d};. Then S(d1) ⊃ S(d2) for d1 < d2, and S(1) contains only the identity mapping. It is obvious that d is the “Koebe constant” for S(d). The relation between d and the second coefficient a2 has been studied by E. Netanyahu [5, 6].

scholarly journals New Symmetric Differential and Integral Operators Defined in the Complex Domain

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 906 ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Function Theory ◽  
Open Unit ◽  
Open Unit Disk ◽  
Geometric Function ◽  
Ruscheweyh Derivative ◽  
Symmetry Properties ◽  
Statistical Studies ◽  
Ordinary Derivative

The symmetric differential operator is a generalization operating of the well-known ordinary derivative. These operators have advantages in boundary value problems, statistical studies and spectral theory. In this effort, we introduce a new symmetric differential operator (SDO) and its integral in the open unit disk. This operator is a generalization of the Sàlàgean differential operator. Our study is based on geometric function theory and its applications in the open unit disk. We formulate new classes of analytic functions using SDO depending on the symmetry properties. Moreover, we define a linear combination operator containing SDO and the Ruscheweyh derivative. We illustrate some inclusion properties and other inequalities involving SDO and its integral.

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