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.

scholarly journals Subordination and Superordination Results for Normalized Analytic Functions Associated with Frasin Operator

2019 ◽  
pp. 37-49
Author(s):  
Abbas Kareem Wanas ◽  
Sibel Yalçin
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
First Order ◽  
Differential Subordination And Superordination

In this paper, we derive some applications of first order differential subordination and superordination results involving Frasin operator for analytic functions in the open unit disk. Also by these results, we obtain sandwich results. Our results extend corresponding previously known results.

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.

scholarly journals New and Extended Results On Fourth-Order Differential Subordination for Univalent Analytic Functions

2020 ◽  
Vol 25 (2) ◽  
pp. 1-13 ◽  
Author(s):  
Waggas Galib Atshan ◽  
Ali Hussein Battor ◽  
Abeer Farhan Abaas ◽  
Georgia Irina Oros
Keyword(s):  
Linear Operator ◽  
Unit Disk ◽  
Fourth Order ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Differential Subordination And Superordination

In this paper, we introduce new concept that is fourth-order differential subordination and superordination associated with linear operator for univalent analytic functions in open unit disk. Here, we extended some lemmas. Also  some interesting new results are obtained.

scholarly journals Some Subordination and Superordination Results for Normalized Analytic Functions Defined by Convolution Structure Associated with Wanas Differential Operator

2020 ◽  
pp. 115-127
Author(s):  
Abbas Kareem Wanas ◽  
Alb Lupas Alina
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Open Unit ◽  
Open Unit Disk ◽  
Convolution Structure

The purpose of this paper is to establish some subordination and superordination results involving Hadamard product for certain normalized analytic functions associated with Wanas differential operator defined in the open unit disk and obtain sandwich results. Our results extend corresponding previously known results.

scholarly journals On a subclass of analytic functions of fractal power with negative coefficients

2021 ◽  
Vol 13(62) (2) ◽  
pp. 387-398
Author(s):  
Zainab E. Abdulnaby ◽  
Rabha W. Ibrahim
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Open Unit ◽  
Open Unit Disk ◽  
Fractal Function ◽  
General Family ◽  
Fractional Differential Operator ◽  
Fractional Differential

The purpose of this article is to introduce a new general family of normalized analytic fractal function in the open unit disk. We employ this class to define a fractional differential operator of two fractals. This operator, under some conditions involves the well known Salagean differential operator. Our method is based on the Hadamard product and its generalization of functions with negative coeffcients.

scholarly journals Differential subordination and superordination results for certain subclasses of analytic functions by the technique of admissible functions

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2009-2026
Author(s):  
R. Jayasankar ◽  
Maslina Darus ◽  
S. Sivasubramanian
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Sandwich Type ◽  
Differential Subordination And Superordination ◽  
Admissible Functions

By investigating appropriate classes of admissible functions, various Differential subordination and superordination results for analytic functions in the open unit disk are obtained using Cho-Kwon-Srivastava operator. As a consequence of these results, Sandwich-type results are also obtained.

scholarly journals Some Subordination Results for Fractional Integral Involving Wanas Differential Operator

2020 ◽  
pp. 199-205
Author(s):  
Abbas Kareem Wanas
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Fractional Integral ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk

In the present paper, we establish some differential subordination properties for analytic functions defined in the open unit disk associated with the fractional integral by using Wanas differential operator.

scholarly journals Strong Differential Subordination Results for Multivalent Analytic Functions Associated with Dziok-Srivastava Operator

2019 ◽  
pp. 159-168
Author(s):  
Abbas Kareem Wanas ◽  
Hala Abbas Mehdi
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Closed Unit Disk ◽  
Strong Differential Subordination

In this paper, by making use of the principle of strong subordination, we establish some interesting properties of multivalent analytic functions defined in the open unit disk and closed unit disk of the complex plane associated with Dziok-Srivastava operator.

LIMITS OF FRACTIONAL DERIVATIVES AND COMPOSITIONS OF ANALYTIC FUNCTIONS

2016 ◽  
Vol 103 (1) ◽  
pp. 104-115 ◽  
Author(s):  
THOMAS H. MACGREGOR ◽  
MICHAEL P. STERNER
Keyword(s):  
Fractional Derivative ◽  
Unit Disk ◽  
Power Function ◽  
Complex Plane ◽  
Analytic Functions ◽  
Fractional Derivatives ◽  
Hadamard Product ◽  
Open Unit ◽  
Open Unit Disk

Suppose that the function $f$ is analytic in the open unit disk $\unicode[STIX]{x1D6E5}$ in the complex plane. For each $\unicode[STIX]{x1D6FC}>0$ a function $f^{[\unicode[STIX]{x1D6FC}]}$ is defined as the Hadamard product of $f$ with a certain power function. The function $f^{[\unicode[STIX]{x1D6FC}]}$ compares with the fractional derivative of $f$ of order $\unicode[STIX]{x1D6FC}$. Suppose that $f^{[\unicode[STIX]{x1D6FC}]}$ has a limit at some point $z_{0}$ on the boundary of $\unicode[STIX]{x1D6E5}$. Then $w_{0}=\lim _{z\rightarrow z_{0}}f(z)$ exists. Suppose that $\unicode[STIX]{x1D6F7}$ is analytic in $f(\unicode[STIX]{x1D6E5})$ and at $w_{0}$. We show that if $g=\unicode[STIX]{x1D6F7}(f)$ then $g^{[\unicode[STIX]{x1D6FC}]}$ has a limit at $z_{0}$.

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.

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