Some analytical merits of Kummer-Type function associated with Mittag-Leffler parameters

Ghanim, F.; Al‐Janaby, Hiba F.

doi:10.1080/25765299.2021.1930637

Cited by 11 publications

(7 citation statements)

References 43 publications

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“…Applying fractional calculus to the Mittag-Leffler function and confluent hypergeometric functions, new results were obtained in [30] regarding the Mittag-Leffler-confluent hypergeometric function. In [31], the authors applied fractional calculus to special functions to define and investigate new variants of the Gamma and Kummer functions for Mittag-Leffler functions. The Caputo-Katugampola fractional derivative was introduced and used to study a new class of fractional Volterra-Fredholm integro-differential equations in [32].…”

Section: Introductionmentioning

confidence: 99%

New Results on a Fractional Integral of Extended Dziok–Srivastava Operator Regarding Strong Subordinations and Superordinations

Lupaş

2023

Symmetry

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In 2012, new classes of analytic functions on U×U¯ with coefficient holomorphic functions in U¯ were defined to give a new approach to the concepts of strong differential subordination and strong differential superordination. Using those new classes, the extended Dziok–Srivastava operator is introduced in this paper and, applying fractional integral to the extended Dziok–Srivastava operator, we obtain a new operator Dz−γHmlα1,β1 that was not previously studied using the new approach on strong differential subordinations and superordinations. In the present article, the fractional integral applied to the extended Dziok–Srivastava operator is investigated by applying means of strong differential subordination and superordination theory using the same new classes of analytic functions on U×U¯. Several strong differential subordinations and superordinations concerning the operator Dz−γHmlα1,β1 are established, and the best dominant and best subordinant are given for each strong differential subordination and strong differential superordination, respectively. This operator may have symmetric or asymmetric properties.

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Section: Introductionmentioning

confidence: 99%

New Results on a Fractional Integral of Extended Dziok–Srivastava Operator Regarding Strong Subordinations and Superordinations

Lupaş

2023

Symmetry

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“…64, No. 10, pp: 5228-5240 5229 The interest in special function theory and its dynamic role in the study of complex analysis [1,2,3], mainly, in geometric function theory (GFT). After employing a hypergeometric function in the verification of a considerable problem in GFT, namely Bieberbach's conjecture [4], this theory motivates the evolution of GFT by captivating numerous scientists to the current research related to operator theory and making worthy contributions [5,6].…”

Section: Introduction Issn: 0067-2904mentioning

confidence: 99%

Sandwich Subordinations Imposed by New Generalized Koebe-Type Operator on Holomorphic Function Class

Moureh,

Al-Janaby

2023

Iraqi Journal of Science

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In the complex field, special functions are closely related to geometric holomorphic functions. Koebe function is a notable contribution to the study of the geometric function theory (GFT), which is a univalent function. This sequel introduces a new class that includes a more general Koebe function which is holomorphic in a complex domain. The purpose of this work is to present a new operator correlated with GFT. A new generalized Koebe operator is proposed in terms of the convolution principle. This Koebe operator refers to the generality of a prominent differential operator, namely the Ruscheweyh operator. Theoretical investigations in this effort lead to a number of implementations in the subordination function theory. The tight upper and lower bounds are discussed in the sense of subordinate structure. Consequently, the subordinate sandwich is acquired. Moreover, certain relevant specific cases are examined.

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“…Various analytic implementations of the integral equations were also investigated. The analysis in [39] focused on the study of special functions combined with fractional calculus and aimed to introduce and further explore novel variants of the Gamma and Kummer functions in terms of Mittag-Leffler functions.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Differential Subordination and Superordination Results for Fractional Integral Associated with Dziok-Srivastava Operator

Lupaş

2023

Mathematics

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Fuzzy set theory, introduced by Zadeh, gives an adaptable and logical solution to the provocation of introducing, evaluating, and opposing numerous sustainability scenarios. The results described in this article use the fuzzy set concept embedded into the theories of differential subordination and superordination from the geometric function theory. In 2011, fuzzy differential subordination was defined as an extension of the classical notion of differential subordination, and in 2017, the dual concept of fuzzy differential superordination appeared. These dual notions are applied in this paper regarding the fractional integral applied to Dziok–Srivastava operator. New fuzzy differential subordinations are proved using known lemmas, and the fuzzy best dominants are established for the obtained fuzzy differential subordinations. Dual results regarding fuzzy differential superordinations are proved for which the fuzzy best subordinates are shown. These are the first results that link the fractional integral applied to Dziok–Srivastava operator to fuzzy theory.

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Some analytical merits of Kummer-Type function associated with Mittag-Leffler parameters

Cited by 11 publications

References 43 publications

New Results on a Fractional Integral of Extended Dziok–Srivastava Operator Regarding Strong Subordinations and Superordinations

New Results on a Fractional Integral of Extended Dziok–Srivastava Operator Regarding Strong Subordinations and Superordinations

Sandwich Subordinations Imposed by New Generalized Koebe-Type Operator on Holomorphic Function Class

Fuzzy Differential Subordination and Superordination Results for Fractional Integral Associated with Dziok-Srivastava Operator

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