On $ q $-analogue of meromorphic multivalent functions in lemniscate of Bernoulli domain

Ahmad, Bakhtiar; Khan, Muhammad Ghaffar; Frasin, B. A.; Aouf, M. K.; Abdeljawad, Thabet; Mashwani, Wali Khan; Arif, Muhammad

doi:10.3934/math.2021185

Cited by 24 publications

(17 citation statements)

References 28 publications

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“…Let us suppose that the first inequality ( 16) holds. en, to show that f is in the class M P,Q (p, α, L, M), we will prove inequality (12). For this, consider…”

Section: Journal Of Mathematicsmentioning

confidence: 96%

“…Similarly, the trend was carried to meromorphic functions by various researchers. Ahmad et al [12] gave the investigation of q-analogue of meromorphic multivalent functions in lemniscate of Bernoulli domain and obtained some interesting results. Arif and Ahmad [13] introduced and studied q-analogue of a meromorphic multivalent operator and presented some interested results.…”

Section: Introduction and Definitionsmentioning

confidence: 99%

See 1 more Smart Citation

Applications of Some Generalized Janowski Meromorphic Multivalent Functions

Ahmad¹,

Khan²,

Darus³

et al. 2021

Journal of Mathematics

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In this article, the ideas of post-quantum calculus and meromorphic multivalent functions are combined and some applications of these functions are discussed. We introduce a new subclass of meromorphic multivalent functions in association with Janowski domain. We investigate and study some useful geometric properties of this class of functions such as sufficiency criteria, distortion problem, growth theorem, radii of starlikeness and convexity, convex combination, and coefficient estimates for this class.

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“…Let us suppose that the first inequality ( 16) holds. en, to show that f is in the class M P,Q (p, α, L, M), we will prove inequality (12). For this, consider…”

Section: Journal Of Mathematicsmentioning

confidence: 96%

Section: Introduction and Definitionsmentioning

confidence: 99%

Applications of Some Generalized Janowski Meromorphic Multivalent Functions

Ahmad¹,

Khan²,

Darus³

et al. 2021

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…It has been used to model engineering and physical processes that are found to be best described by fractional differential equations. Fractional order derivatives [26] , [27] are useful in demonstrating many natural facts and phenomena having non-local complex dynamical behavior. These operators are helpful to overcome all the restrictions on the order of differential equations while solving them.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of Atangana-Baleanu fractional model to understand the propagation of a novel corona virus pandemic

Butt

Ahmad

Rafiq

et al. 2022

Alexandria Engineering Journal

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In this manuscript, we formulated a new nonlinear SEIQR fractional order pandemic model for the Corona virus disease (COVID-19) with Atangana-Baleanu derivative. Two main equilibrium points of the proposed model are stated. Threshold parameter for the model using next generation technique is computed to investigate the future dynamics of the disease. The existence and uniqueness of solution is proved using a fixed point theorem. For the numerical solution of fractional model, we implemented a newly proposed Toufik-Atangana numerical scheme to validate the importance of arbitrary order derivative and our obtained theoretical results. It is worth mentioning that fractional order derivative provides much deeper information about the complex dynamics of Corona model. Results obtained through the proposed scheme are dynamically consistent and good in agreement with the analytical results. To draw our conclusions, we explore a complete quantitative analysis of the given model for different quarantine levels. It is claimed through numerical simulations that pandemic could be eradicated faster if a human community selfishly adopts mandatory quarantine measures at various coverage levels with proper awareness. Finally, we have executed the joint variability of all classes to understand the effectiveness of quarantine policy on human population.

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“…Very recently, by using q-Deference operator, Srivastava et al [14] studied a certain subclass of analytic function with symmetric points. Several other authors (see, for example, [15][16][17][18][19][20][21][22]) have studied and generalized the classes of symmetric and other q-starlike functions from different viewpoints and perspectives. For some more recent investigation about q-calculus, we may refer the interested reader to [23,24].…”

Section: Introduction Definitions and Motivationmentioning

confidence: 99%

Coefficient Estimates for a Subclass of Meromorphic Multivalent q-Close-to-Convex Functions

Shi

Ahmad²,

Khan

et al. 2021

Symmetry

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By making use of the concept of basic (or q-) calculus, many subclasses of analytic and symmetric q-starlike functions have been defined and studied from different viewpoints and perspectives. In this article, we introduce a new class of meromorphic multivalent close-to-convex functions with the help of a q-differential operator. Furthermore, we investigate some useful properties such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity for this new subclass.

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On $ q $-analogue of meromorphic multivalent functions in lemniscate of Bernoulli domain

Cited by 24 publications

References 28 publications

Applications of Some Generalized Janowski Meromorphic Multivalent Functions

Applications of Some Generalized Janowski Meromorphic Multivalent Functions

Numerical analysis of Atangana-Baleanu fractional model to understand the propagation of a novel corona virus pandemic

Coefficient Estimates for a Subclass of Meromorphic Multivalent q-Close-to-Convex Functions

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