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

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Najla M. Alarifi ◽  
Rabha W. Ibrahim
Keyword(s):  
Differential Operator ◽  
Differential Operators ◽  
Integral Operators ◽  
Real Variable ◽  
Open Unit ◽  
New Class ◽  
Science Technology ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Fractional Differential Operators

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.

scholarly journals Modelling chaotic dynamical attractor with fractal-fractional differential operators

2021 ◽  
Vol 6 (12) ◽  
pp. 13689-13725
Author(s):  
Sonal Jain ◽  
◽  
Youssef El-Khatib
Keyword(s):  
Dynamical System ◽  
Fractal Dimension ◽  
Fractional Order ◽  
Differential Operators ◽  
Chaotic Behavior ◽  
Integral Operators ◽  
Great Success ◽  
New Class ◽  
Fractional Differential ◽  
Fractional Differential Operators

<abstract><p>Differential operators based on convolution have been recognized as powerful mathematical operators able to depict and capture chaotic behaviors, especially those that are not able to be depicted using classical differential and integral operators. While these differential operators have being applied with great success in many fields of science, especially in the case of dynamical system, we have to confess that they were not able depict some chaotic behaviors, especially those with additionally similar patterns. To solve this issue new class of differential and integral operators were proposed and applied in few problems. In this paper, we aim to depict chaotic behavior using the newly defined differential and integral operators with fractional order and fractal dimension. Additionally we introduced a new chaotic operators with strange attractors. Several simulations have been conducted and illustrations of the results are provided to show the efficiency of the models.</p></abstract>

scholarly journals On Multivalent Analytic Functions Considered by a Multi-Arbitrary Differential Operator in a Complex Domain

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 315
Author(s):  
Najla M. Alarifi ◽  
Rabha W. Ibrahim
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Integral Operators ◽  
Upper And Lower Bounds ◽  
Fractional Operator ◽  
Convolution Operators ◽  
Linear Convolution ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Special Case

(1) Background: There is an increasing amount of information in complex domains, which necessitates the development of various kinds of operators, such as differential, integral, and linear convolution operators. Few investigations of the fractional differential and integral operators of a complex variable have been undertaken. (2) Methods: In this effort, we aim to present a generalization of a class of analytic functions based on a complex fractional differential operator. This class is defined by utilizing the subordination and superordination theory. (3) Results: We illustrate different fractional inequalities of starlike and convex formulas. Moreover, we discuss the main conditions to obtain sandwich inequalities involving the fractional operator. (4) Conclusion: We indicate that the suggested class is a generalization of recent works and can be applied to discuss the upper and lower bounds of a special case of fractional differential equations.

An Improved Fractional Differential Algorithm and Noise Immunity Analysis

2011 ◽  
Vol 121-126 ◽  
pp. 710-714
Author(s):  
Yu Ran Liu ◽  
Ming Liang Hou
Keyword(s):  
Differential Operator ◽  
Noise Immunity ◽  
Differential Operators ◽  
Natural Images ◽  
Edge Information ◽  
Integer Order ◽  
Texture Information ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Differential Algorithm

Texture and edge information are equally important to identification of most of natural images. To the problem of the existing integer order differential operators can’t extract texture information form the images, this study developed a fractional differential algorithm, which can extract texture and marginal information simultaneously, based on settlement of the drift problem of fractional differential operator. Experimental results showed that our algorithm can not only extract texture information but also extract more edge information than the traditional algorithms. And to the image with Gauss noise, our algorithm also have noise immunity.

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 On multi-order fractional differential operators in the unit disk

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 73-81 ◽  
Author(s):  
Rabha Ibrahim ◽  
Cenap Ozel
Keyword(s):  
Unit Disk ◽  
Differential Operators ◽  
Analytic Formula ◽  
Fractional Operators ◽  
Multi Index ◽  
Owa Operators ◽  
Generalized Wright Function ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Fractional Differential Operators

In this article, we generalize fractional operators (differential and integral) in the unit disk. These operators are generalized the Srivastava-Owa operators. Geometric properties are studied and the advantages of these operators are discussed. As an application, we impose a method, involving a memory formalism of the Beer-Lambert equation based on a new generalized fractional differential operator. We give solutions in terms of the multi-index Mittag-Leffler function. In addition, we sanctify the out come from a stochastic standpoint. We utilize the generalized Wright function to obtain the analytic formula of solutions.

scholarly journals Splines and fractional differential operators

2020 ◽  
pp. 2040005
Author(s):  
Peter Massopust
Keyword(s):  
Differential Operator ◽  
Differential Operators ◽  
Linear Differential Operator ◽  
Operator Equations ◽  
B Splines ◽  
Linear Differential Operators ◽  
Fractional Differential ◽  
Linear Differential ◽  
Fractional Differential Operators ◽  
Integral Order

Several classes of classical cardinal B-splines can be obtained as solutions of operator equations of the form [Formula: see text] where [Formula: see text] is a linear differential operator of integral order. In this paper, we consider classes of generalized B-splines consisting of cardinal polynomial B-splines of complex and hypercomplex orders and cardinal exponential B-splines of complex order and derive the fractional linear differential operators that are naturally associated with them. For this purpose, we also present the spaces of distributions onto which these fractional differential operators act.

scholarly journals Study of new class of q-fractional integral operator

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5713-5721
Author(s):  
M. Momenzadeh ◽  
N.I. Mahmudov
Keyword(s):  
Differential Operator ◽  
Integral Operator ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Integral Approach ◽  
Cauchy Integral ◽  
New Class ◽  
Fractional Differential Operator ◽  
Fractional Differential

In this paper, we study on the new class of q-fractional integral operator. In the aid of iterated Cauchy integral approach to fractional integral operator, we applied tp f(t) in these integrals and a new class of q-fractional integral operator with parameter p, is introduced. Recently, the q-analogue of fractional differential integral operator is studied and all of the operators defined in these studies are q-analogue of Riemann fractional differential operator. We show that our new class of operator generalize all the operators in use, and additionally, it can cover the q-analogue of Hadamard fractional differential operator, as well. Some properties of this operator are investigated.

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.

On the Influence of Fractional Derivative on Chaos Control of a New Fractional-Order Hyperchaotic System

2020 ◽  
pp. 115-132
Author(s):  
Ahmed Ezzat Mohamed Matouk
Keyword(s):  
Differential Operator ◽  
Fractional Order ◽  
Differential Operators ◽  
Equilibrium Points ◽  
Hyperchaotic System ◽  
Fractional Differential Operator ◽  
Quadratic Nonlinearities ◽  
Potential Applications ◽  
Non Local ◽  
Fractional Differential

The non-local fractional differential operators have potential applications in many fields of science and technology but especially in the field of dynamical systems. This chapter introduces a new hyperchaotic dynamical system involving non-local fractional differential operator with singular kernel (the Caputo type). The system involves three quadratic nonlinearities and also three equilibrium points. Existence of chaotic and hyperchaotic attractors has been illustrated. Based on Matouk's stability theory of four-dimensional fractional-order systems, the influence of the fractional differential operator on stabilizing the proposed system to its three steady states has been shown. Numerical results have been provided to verify the theoretical analysis. This kind of study is expected to add useful applications to chaos-based secure communications and text encryption.

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