Differential subordination results for Mittag-Leffler type functions with bounded turning property

Al‐Janaby, Hiba F.; Darus, Maslina

doi:10.1515/ms-2017-0248

Cited by 6 publications

(3 citation statements)

References 23 publications

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“…In effect, interesting recent studies have emanated about dealing with subordinate and superordinate techniques and sandwiches problems correlated with numerous complex operators, for instance, Atshan et al [17], Sokół et al [18], Zayed and Bulboacă [19], Al-Janaby and Ahmad [20], Mishra and Soren [21], Al-Janaby and Darus [22], Al-Janaby et al ( [23], [24]), Ghanim and Al-Janaby ( [25], [26]), Attiy ([27], [28]), Lupaş and Oros [29] and Atshan ( [30], [31]).…”

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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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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“…Furthermore, derivations of physical phenomena of exponential nature could be determined by the physical laws via the M-LTF (power-law), (Bhatter, Mathur, Kumar, Nisar, & Singh, 2020;Djida, Mophou, &Area, 2019 andSaqib, Khan, &Shafie, 2019). Due to successful diverse applications for M-LTFs, correlated with FC, in physics and mathematic allied problems, several researchers prompted a lot of attention to the behaviour of M-LTFs and extended their outcomes to the complex domain, (for instance, see Al-Janaby, 2018;Al-Janaby & Ahmad, 2018;Al-Janaby &Darus, 2019 andNisar, 2019).…”

Section: Introductionmentioning

confidence: 99%

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

Ghanim

Al‐Janaby

2021

Arab Journal of Basic and Applied Sciences

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As of late, the study of Fractional Calculus (FC) and Special Functions (SFs) has been interestingly prompted in various realms of mathematics, engineering and sciences. This is due to the considerable demonstrated potential of their applications. Among these SFs, Gamma function and Mittag-Leffler functions are the most renowned and distinguished. Numerous authors continue to study this line. The current analysis attempts to introduce and further examine new modifications of Gamma and Kummer function in terms of Mittag-Leffler functions, respectively. Several attributes and formulations of this new Kummer-type function that include integral representations, Beta transform, Laplace transform, derivative formulas, and recurrence relation are investigated. Furthermore, outcomes of Riemann-Liouville fractional integral and fractional derivative in relation to this newly established Kummer function are also investigated.

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“…Actually, the analysis of M-LF and its various formulas have attracted considerable interest, and many researchs has thereafter emerged on this topic. For instance, Srivastava et al ( [31], [35]), Rahman et al [24], Agarwal et al [1], Al-Janaby [3], Al-Janaby and Ahmad [4], Al-Janaby and Darus [5] and others.…”

Section: Introductionmentioning

confidence: 99%

Inclusion and convolution features of univalent meromorphic functions correlating with Mittag-Leffler function

Ghanim

Al-Janaby

2020

Filomat

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The so-called Mittag-Leffler function (M-LF) provides solutions to the fractional differential or integral equations with numerous implementations in applied sciences and other allied disciplines. During the previous century, the interest in M-LF has significantly developed and a variety of extensions and generalizations forms of the M-LF have been posed. Moreover, M-LF played a distinguished and important role in Geometric Function Theory (GFT). The intent of the current study is to reveal various inclusion and convolution features for a specific subclass of univalent meromorphic functions correlating with the integrodifferential operator containing an extended generalized M-LF. Some consequences of the major geometric outcomes are also presented.

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Differential subordination results for Mittag-Leffler type functions with bounded turning property

Abstract: We aim to present a new linear integral operator and a certain subclass of regular functions with bounded turning property in correlation with the extended generalised Mittag-Leffler functions. Several results concerning an application of differential subordination are also investigated.

Cited by 6 publications

References 23 publications

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

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

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

Inclusion and convolution features of univalent meromorphic functions correlating with Mittag-Leffler function

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