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On some properties of the bibasic Humbert hypergeometric functions Ξ_(1) and Ξ_(2)

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Applied Mathematics(A Journal of Chinese Universities) 2023年第4期38卷 614-630页

作者： CAI qing-bo Ghazi S.Khammash Shimaa I.Moustafa Ayman Shehata Provincial Key Laboratory of Data-Intensive Computing Key Laboratory of Intelligent Computing and Information ProcessingSchool of Mathematics and Computer ScienceQuanzhou Normal UniversityQuanzhou 362000China Department of Mathematics Al-Aqsa UniversityGazaGaza StripPalestine Department of Mathematics Faculty of ScienceAssiut UniversityAssiut 71516Egypt Department of Mathematics Unaizah College of Science and ArtsUnaizah 56264Qassim UniversityBuraydah 52571QassimSaudi Arabia

The main object of this paper is to deduce the bibasic Humbert functions Ξ_(1) and Ξ_(2)Some interesting results and elementary summations technique that was successfully employed,q-recursion,q-derivatives relations,the q-differential recursion relations,the q-integral representations for Ξ_(1) and Ξ_(2)are *** summation formula derives a list of p-analogues of transformation formulas for bibasic Humbert functions that have been studied,also some hypergeometric functions properties of some new interesting special cases have been given.

关键词： q-calculus bibasic Humbert hypergeometric functions q-derivative

Note on a New Construction of Kantorovich Form q-Bernstein Operators Related to Shape Parameter λ

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Computer Modeling in Engineering & Sciences 2022年第3期130卷 1479-1493页

作者： qingbo Cai Resat Aslan Fujian Provincial Key Laboratory of Data-Intensive Computing Key Laboratory of Intelligent Computing and Information ProcessingSchool of Mathematics and Computer ScienceQuanzhou Normal UniversityQuanzhou362000China Department of Mathematics Faculty of Sciences and ArtsHarran UniversitySanlıurfa63300Turkey

The main purpose of this paper is to introduce some approximation properties of a Kantorovich kind q-Bernstein operators related to B′ezier basis functions with shape parameterλ∈[−1,1].Firstly,we compute some basic results such as moments and central moments,and derive the Korovkin type approximation theorem for these ***,we estimate the order of convergence in terms of the usual modulus of continuity,for the functions belong to Lipschitz-type class and Peetre’s K-functional,***,with the aid of Maple software,we present the comparison of the convergence of these newly defined operators to the certain function with some graphical illustrations and error estimation table.

关键词： q-calculus (λ,q)-Bernstein polynomials order of convergence Lipschitz-type function Peetre’s K-functional

Partial sums of generalized harmonic starlike univalent functions generated by a (p,q)−Ruscheweyh-type harmonic differential operator

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Applied Mathematics(A Journal of Chinese Universities) 2024年第4期39卷 584-595页

作者： Om P Ahuja Asena Cetinkaya Raj Kumar Department of Mathematical Sciences Kent State UniversityOhio44021USA Department of of Mathematics and Computer Science Istanbul Kultur UniversityIstanbulTurkey Department of of Mathematics DAV UniversityJalandharIndia

Let H denote the class of complex-valued harmonic functions f defined in the open unit disc D and normalized by f(0)=fz(0)-1=*** this paper,we define a new generalized subclass of H associated with the(p,q)-Ruscheweyh-type harmonic differential operator in *** first obtain a sufficient coefficient condition that guarantees that a function f in H is sense-preserving harmonic univalent in D and belongs to the aforementioned *** this coefficient condition,we then examine ratios of partial sums of f in *** all cases the results are *** addition,the results so obtained generalize the related works of some authors,and many other new results are obtained.

关键词： (p,q)-calculus (p,q)-derivative operator q-calculus q-derivative operator (p,q)-Ruscheweyhtype harmonic differential operator partial sums coefficient estimate

An extensive analytical and numerical study of the generalized q-deformed Sinh-Gordon equation

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Journal of Ocean Engineering and Science 2024年第3期9卷 232-239页

作者： Khalid K.Ali Abdel-Haleem Abdel-Aty Mathematics Department Faculty of ScienceAl-Azhar UniversityNasr-CityCairoEgypt Department of Physics College of SciencesUniversity of BishaPO Box 344Bisha 61922Saudi Arabia Physics Department Faculty of ScienceAl-Azhar UniversityAssiut 71524Egypt

In this paper,the q-deformed Sinh-Gordon equation is solved analytically using a new general form based on the extended tanh *** numerical solutions of the equation is obtained using a b-spline finite element ***,we present numerous figures to demonstrate the various solitons propagation *** type of equation has not been previously dealt with in such ways,whether analytical or *** study is very useful in studying several physical systems that have lost their symmetry.

关键词： q-Deformed equation Solitos solutions The extended tanh method Finite element method q-calculus

(p,q)-Analogue of Mittag-Leffler Function with(p,q)-Laplace Transform

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Analysis in Theory and Applications 2022年第3期38卷 351-360页

作者： Alok Jain Altaf Ahmad Bhat Renu Jain Deepak Kumar Jain School of Mathematics and Allied Sciences Jiwaji UniversityGwalior(M.P.)India Department of Mathematical Sciences Islamic University of Science and TechnologyAwantipora PulwamaJand KIndia-192122 Department of Engineering Mathematics and Computing MITSGwalior(M.P.)India

The aim of this paper is to define(p,q)-analogue of Mittag-Leffler Function,by using(p,q)-Gamma *** transformation formulae are also derived by using the(p,q)-***(p,q)-analogue for this function provides elegant generalization of q-analogue of Mittag-Leffler function in connection with ***,the(p,q)-Laplace Transform of the Mittag-Leffler function has been *** special cases have also been discussed.

关键词： (p,q)-analogue of Mittag-Leffler function (p,q)-Gamma function q-calculus (p,q)-derivative operator (p,q)-Laplace transform