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Natural transform of two variables in q-calculus with applications
Bollettino dell'Unione Matematica Italiana, 2023The authors introduce the double \(q\)-natural transform, a \(q\)-analogue of the double natural transform of a function \( f(x,y) \), with \( x, y \geq 0 \), defined by \[ N_2^+\{f(x,y)\} = \frac{1}{uv} \int_0^{\infty}\quad \int_0^{\infty} \mathrm{e}^{-sx/u-ty/v} f(x,y)\;\mathrm{d} x\, \mathrm{d} y.
Ganie, Javid Ahmad +2 more
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2013
In the field of approximation theory, the applications of q-calculus are new area in last 25 years. The first q-analogue of the well-known Bernstein polynomials was introduced by Lupas in the year 1987. In 1997 Phillips considered another q-analogue of the classical Bernstein polynomials.
Ali Aral, Vijay Gupta, Ravi P. Agarwal
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In the field of approximation theory, the applications of q-calculus are new area in last 25 years. The first q-analogue of the well-known Bernstein polynomials was introduced by Lupas in the year 1987. In 1997 Phillips considered another q-analogue of the classical Bernstein polynomials.
Ali Aral, Vijay Gupta, Ravi P. Agarwal
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A possible generalization Shannon’s entropy using q-calculus
Journal of Mathematical Chemistry, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Iranian Journal of Science and Technology, Transactions A: Science, 2020
Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and basic (or q-) hypergeometric polynomials, are known to have widespread applications, particularly in several areas of number theory and combinatorial analysis such as (for example) the theory of partitions.
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Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and basic (or q-) hypergeometric polynomials, are known to have widespread applications, particularly in several areas of number theory and combinatorial analysis such as (for example) the theory of partitions.
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Frustrated spin models an the q-calculus
Le Journal de Physique IV, 1998We present the solution of the (ganged) frustrated Spherical Model, which is obtained by using q-polynomials. This is a first step towards the solution of the physically relevant frustrated XY model, a deterministic model which may behave as a spin glass.
A. Cappelli, F. Colomo
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2012
We give a systematic summary of the applications of q-analysis in physics in nine separate sections. Each section is about a certain theme, the connection is the quantum group SU q (2). Both the Santilli hadron mechanics and the Wess-Zumino model for elementary particles use q-calculus as a mathematical model.
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We give a systematic summary of the applications of q-analysis in physics in nine separate sections. Each section is about a certain theme, the connection is the quantum group SU q (2). Both the Santilli hadron mechanics and the Wess-Zumino model for elementary particles use q-calculus as a mathematical model.
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On the Solutions of Some Equations in (p, q)-Calculus
2023In this paper, we introduce the Laplace equation in (p, q)-calculus and give the solutions of the equation using the separation method into its variables. We also give the (p, q)-calculus version of the equation of motion, which expresses the displacement of a falling field in a resistant environment.
Turan, Nihan, Basarır, Metin
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The different languages of q-calculus
2012We give a survey of the different schools in q-analysis and introduce difference calculus and Bernoulli numbers to make a preparation for the important fourth chapter. We summarize the different attempts at elliptic and Theta functions, both of which are intimately related to q-calculus.
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Relations Between the Fractional Operators in q-Calculus
2020In this survey paper, we will consider the fractional operators in q-calculus. Starting from the fractional versions of q-Pochhammer symbol, we generalize the notions of the fractional q-integral and q-derivative by introducing variable lower bound of integration.
Sergei Silvestrov +3 more
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Certain inequalities for fractional $(p,q)$-calculus
Advanced Studies: Euro-Tbilisi Mathematical Journal, 2022Jain, Pankaj, Manglik, Rohit
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