A CERTAIN FRACTIONAL DERIVATIVE OPERATOR FOR p-VALENT FUNCTIONS AND NEW CLASS OF ANALYTIC FUNCTIONS WITH NEGATIVE COEFFICIENTS

2015 ◽  
Vol 99 (1) ◽  
pp. 75-87 ◽  
Author(s):  
A. A. Amourah ◽  
Feras Yousef ◽  
Tariq Al-Hawary ◽  
M. Darus
Keyword(s):  
Fractional Derivative ◽  
Analytic Functions ◽  
Derivative Operator ◽  
New Class

scholarly journals Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 172 ◽  
Author(s):  
Hari M. Srivastava ◽  
Ahmad Motamednezhad ◽  
Ebrahim Analouei Adegani
Keyword(s):  
Fractional Derivative ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Faber Polynomial

In this article, we introduce a general family of analytic and bi-univalent functions in the open unit disk, which is defined by applying the principle of differential subordination between analytic functions and the Tremblay fractional derivative operator. The upper bounds for the general coefficients | a n | of functions in this subclass are found by using the Faber polynomial expansion. We have thereby generalized and improved some of the previously published results.

scholarly journals Some Inclusion Properties of Certain Subclasses of Analytic Functions Defined by Using the Tremblay Fractional Derivative Operator

2021 ◽  
Vol 20 ◽  
pp. 209-216
Author(s):  
Fawzan Ismail Sidky ◽  
Doaa Shokry Mohamed ◽  
Amina Ahmed Awad
Keyword(s):  
Fractional Derivative ◽  
Convex Functions ◽  
Analytic Functions ◽  
Derivative Operator ◽  
Operator Inclusion ◽  
Inclusion Properties

In this paper, we introduce new subclasses of analytic and p-valent functions related to starlike, convex, close-to-convex, and quasi-convex functions by using a p-valent analog of the Tremblay fractional derivative operator. Inclusion relationships for these subclasses are established.

scholarly journals On a Generalized Convolution Operator

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2141
Author(s):  
Poonam Sharma ◽  
Ravinder Krishna Raina ◽  
Janusz Sokół
Keyword(s):  
Fractional Derivative ◽  
Convolution Operator ◽  
Analytic Functions ◽  
Linear Operators ◽  
Generalized Convolution ◽  
Derivative Operator ◽  
Special Cases ◽  
Lerch Zeta Function ◽  
The One ◽  
Appell Function

Recently in the paper [Mediterr. J. Math. 2016, 13, 1535–1553], the authors introduced and studied a new operator which was defined as a convolution of the three popular linear operators, namely the Sǎlǎgean operator, the Ruscheweyh operator and a fractional derivative operator. In the present paper, we consider an operator which is a convolution operator of only two linear operators (with lesser restricted parameters) that yield various well-known operators, defined by a symmetric way, including the one studied in the above-mentioned paper. Several results on the subordination of analytic functions to this operator (defined below) are investigated. Some of the results presented are shown to involve the familiar Appell function and Hurwitz–Lerch Zeta function. Special cases and interesting consequences being in symmetry of our main results are also mentioned.

scholarly journals Some applications of generalized Ruscheweyh derivatives involving a general fractional derivative operator to a class of analytic functions with negative coefficients II

2020 ◽  
Vol 28 (1) ◽  
pp. 85-103
Author(s):  
Waggas Galib Atshan ◽  
S. R. Kulkarni
Keyword(s):  
Fractional Derivative ◽  
Linear Combination ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Integral Operators ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Derivative Operator ◽  
Necessary And Sufficient

AbstractIn this paper, we study a class of univalent functions f as defined by making use of the generalized Ruscheweyh derivatives involving a general fractional derivative operator, satisfying{\mathop{\rm Re}\nolimits} \left\{{{{z\left({{\bf{J}}_1^{\lambda,\mu}f\left(z \right)} \right)'} \over {\left({1 - \gamma} \right){\bf{J}}_1^{\lambda,\mu}f\left(z \right) + \gamma {z^2}\left({{\bf{J}}_1^{\lambda,\mu}f\left(z \right)} \right)''}}} \right\} > \beta.A necessary and sufficient condition for a function to be in the class A_\gamma ^{\lambda,\mu,\nu}\left({n,\beta} \right) is obtained. Also, our paper includes linear combination, integral operators and we introduce the subclass A_{\gamma,{c_m}}^{\lambda,\mu,\nu}\left({1,\beta} \right) consisting of functions with negative and fixed finitely many coefficients. We study some interesting properties of A_{\gamma,{c_m}}^{\lambda,\mu,\nu}\left({1,\beta} \right).

scholarly journals An Upper Bound of the Third Hankel Determinant for a Subclass of q-Starlike Functions Associated with k-Fibonacci Numbers

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1043 ◽  
Author(s):  
Muhammad Shafiq ◽  
Hari M. Srivastava ◽  
Nazar Khan ◽  
Qazi Zahoor Ahmad ◽  
Maslina Darus ◽  
...  
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Fibonacci Numbers ◽  
Starlike Functions ◽  
Function Class ◽  
Hankel Determinant ◽  
Derivative Operator ◽  
New Class ◽  
The Third ◽  
Class A

In this paper, we use q-derivative operator to define a new class of q-starlike functions associated with k-Fibonacci numbers. This newly defined class is a subclass of class A of normalized analytic functions, where class A is invariant (or symmetric) under rotations. For this function class we obtain an upper bound of the third Hankel determinant.

scholarly journals ON A CLASS OF FRACTIONAL HARDY-TYPE INEQUALITIES

Fractals ◽  
2021 ◽  
pp. 2240011
Author(s):  
SHANHE WU ◽  
MUHAMMAD SAMRAIZ ◽  
SAJID IQBAL ◽  
GAUHAR RAHMAN
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Fractional Operators ◽  
Hilfer Fractional Derivative ◽  
Derivative Operator ◽  
Hardy Type Inequalities ◽  
New Class ◽  
Hardy Type ◽  
Fractional Calculus Operators

In this paper, we study a new class of Hardy-type inequalities involving fractional calculus operators. We derive the Hardy-type inequalities for the variant of Riemann–Liouville fractional calculus operators and [Formula: see text]-Hilfer fractional derivative operator. The obtained inequalities involving fractional operators are more general as compared to some existing results in the literature.

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