scholarly journals Time-Space Fractional Heat Equation in the Unit Disk

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Hamid A. Jalab
Keyword(s):  
Heat Equation ◽  
Unit Disk ◽  
Hypergeometric Functions ◽  
Univalent Functions ◽  
Maximal Solution ◽  
Owa Operator ◽  
Generalized Hypergeometric Functions ◽  
Fractional Heat Equation ◽  
Time Space ◽  
Fractional Space

We will study a maximal solution of the time-space fractional heat equation in complex domain. The fractional time is taken in the sense of the Riemann-Liouville operator, while the fractional space is assumed in the Srivastava-Owa operator. Here we employ some properties of the univalent functions in the unit disk to determine the upper bound of this solution. The maximal solution is illustrated in terms of the generalized hypergeometric functions.

scholarly journals Subclasses of Analytic Functions Defined by Generalized Hypergeometric Functions

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Badr S. Alkahtani ◽  
Saima Mustafa ◽  
Teodor Bulboacă
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Generalized Hypergeometric Functions ◽  
Radius Problems ◽  
Inclusion Results

We introduce a new subclass of analytic functions in the unit diskU, defined by using the generalized hypergeometric functions, which extends some previous well-known classes defined by different authors. Inclusion results, radius problems, and some connections with the Bernardi-Libera-Livingston integral operator are discussed.

scholarly journals The Pre-Schwarzian Norm Estimate for Analytic Concave Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Young Jae Sim ◽  
Oh Sang Kwon
Keyword(s):  
Unit Disk ◽  
Hypergeometric Functions ◽  
Hadamard Product ◽  
Univalent Functions ◽  
Open Unit ◽  
Opening Angle ◽  
Sufficient Condition ◽  
Open Unit Disk ◽  
Concave Functions ◽  
Norm Estimate

LetDdenote the open unit disk and letSdenote the class of normalized univalent functions which are analytic inD. LetCo(α)be the class of concave functionsf∈S, which have the condition that the opening angle off(D)at infinity is less than or equal toπα,α∈(1,2]. In this paper, we find a sufficient condition for the Gaussian hypergeometric functions to be in the classCo(α). And we define a classCo(α,A,B),(-1≤B<A≤1), which is a subclass ofCo(α)and we find the set of variabilities for the functional(1-|z|2)(f″(z)/f′(z))forf∈Co(α,A,B). This gives sharp upper and lower estimates for the pre-Schwarzian norm of functions inCo(α,A,B). We also give a characterization for functions inCo(α,A,B)in terms of Hadamard product.

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 Inclusion Relation between Various Subclasses of Harmonic Univalent Functions Associated with Wright’s Generalized Hypergeometric Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Rajavadivelu Themangani ◽  
Saurabh Porwal ◽  
Nanjundan Magesh
Keyword(s):  
Hypergeometric Functions ◽  
Univalent Functions ◽  
Convolution Operators ◽  
Inclusion Relation ◽  
Generalized Hypergeometric Functions

The purpose of the present paper is to obtain some inclusion relation between various subclasses of harmonic univalent functions by applying certain convolution operators associated with Wright’s generalized hypergeometric functions.

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 Inequalities of harmonic univalent functions with connections of hypergeometric functions

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Janusz Sokół ◽  
Rabha W. Ibrahim ◽  
M. Z. Ahmad ◽  
Hiba F. Al-Janaby
Keyword(s):  
Unit Disk ◽  
Hypergeometric Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disk ◽  
Distortion Bounds ◽  
Class Of Functions

AbstractLet SH be the class of functions f = h+g that are harmonic univalent and sense-preserving in the open unit disk U = { z : |z| < 1} for which f (0) = f'(0)-1=0. In this paper, we introduce and study a subclass H( α, β) of the class SH and the subclass NH( α, β) with negative coefficients. We obtain basic results involving sufficient coefficient conditions for a function in the subclass H( α, β) and we show that these conditions are also necessary for negative coefficients, distortion bounds, extreme points, convolution and convex combinations. In this paper an attempt has also been made to discuss some results that uncover some of the connections of hypergeometric functions with a subclass of harmonic univalent functions.

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