Some properties for integro-differential operator defined by a fractional formal

Abdulnaby, Zainab E.; Ibrahim, Rabha W.; Kılıçman, Adem

doi:10.1186/s40064-016-2563-0

Cited by 7 publications

(2 citation statements)

References 15 publications

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“…Essentially, these operators are used to define, improve, and generalize many well-known analytic function classes in the open unit disk. These studies imply more geometric features for the investigated analytic function classes and preserve many of their properties (see, for example, [1,2,10,26,27]). …”

Section: Introductionmentioning

confidence: 81%

Generalized convolution properties based on the modified Mittag-Leffler function

Srivástava¹,

Kılıçman²,

Abdulnaby³

et al. 2017

J. Nonlinear Sci. Appl.

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Studies of convolution play an important role in Geometric Function Theory (GFT). Such studies attracted a large number of researchers in recent years. By making use of the Hadamard product (or convolution), several new and interesting subclasses of analytic and univalent functions have been introduced and investigated in the direction of well-known concepts such as the subordination and superordination inequalities, integral mean and partial sums, and so on. In this article, we apply the Hadamard product (or convolution) by utilizing some special functions. Our contribution in this paper includes defining a new linear operator in the form of the generalized Mittag-Leffler function in terms of the extensively-investigated Fox-Wright p Ψ qfunction in the right-half of the open unit disk where where (z) > 0. We then show that the new linear convolution operator is bounded in some spaces. In particular, several boundedness properties of this linear convolution operator under mappings from a weighted Bloch space into a weighted-log Bloch space are also investigated. For uniformity and convenience, the Fox-Wright p Ψ q -notation is used in our results.

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Section: Introductionmentioning

confidence: 81%

Generalized convolution properties based on the modified Mittag-Leffler function

Srivástava¹,

Kılıçman²,

Abdulnaby³

et al. 2017

J. Nonlinear Sci. Appl.

Self Cite

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show abstract

“…It is well known that we can make better exact models for most natural phenomena by using fractional differential equations. Most researchers are working on fractional integrodifferential equations (see, for example, [1,2,[5][6][7][8][10][11][12][13][14][15][16][17][18][19][20][21]).…”

Section: Preliminariesmentioning

confidence: 99%

On a three step crisis integro-differential equation

2019

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Upper bound of fractional differential operator related to univalent functions

2016

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In this article, we defined the generalized fractional differential Tremblay operator in the open unit disk that by usage the definition of the generalized SrivastavaOwa operator. In particular, we established a new operator denoted by H b;s;c z based on the normalized generalized fractional differential operator and represented by convolution product. Moreover, we studied the coefficient criteria of univalence, starlikeness and convexity for the last operator mentioned.

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Some properties for integro-differential operator defined by a fractional formal

Cited by 7 publications

References 15 publications

Generalized convolution properties based on the modified Mittag-Leffler function

Generalized convolution properties based on the modified Mittag-Leffler function

On a three step crisis integro-differential equation

Upper bound of fractional differential operator related to univalent functions

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