Results 11 to 20 of about 1,838,482 (246)
The different tongues of q-calculus; pp. 81–99 [PDF]
Proceedings of the Estonian Academy of Sciences, 2008 In this review paper we summarize the various dialects of q-calculus: quantum calculus, time scales, and partitions. The close connection between Îq(x) functions on the one hand, and elliptic functions and theta functions on the other hand will be shown.
Thomas Ernst
doaj +3 more sources
On Iterative Methods for Solving Nonlinear Equations in Quantum Calculus
Fractal and Fractional, 2021 Quantum calculus (also known as the q-calculus) is a technique that is similar to traditional calculus, but focuses on the concept of deriving q-analogous results without the use of the limits.
Gul Sana +4 more
doaj +2 more sources
The homotopy analysis method for q-difference equations
Ain Shams Engineering Journal, 2018 The q-difference equations are kind of important problems in q-calculus and applied mathematics. In this paper, the homotopy analysis method is extended to find approximate solution for some of q-differential equations.
Mourad S. Semary, Hany N. Hassan
doaj +3 more sources
Opial inequality in q-calculus [PDF]
Journal of Inequalities and Applications, 2018 In this article we give q-analogs of the Opial inequality for q-decreasing functions. Using a closed form of the restricted q-integral (see Gauchman in Comput. Math. Appl. 47:281–300, 2004), we establish a new integral inequality of the q-Opial type.
Tatjana Z. Mirković +2 more
doaj +2 more sources
A certain ( p , q ) $(p,q)$ -derivative operator and associated divided differences [PDF]
Journal of Inequalities and Applications, 2016 Recently, Sofonea (Gen. Math. 16:47-54, 2008) considered some relations in the context of quantum calculus associated with the q-derivative operator D q $D_{q}$ and divided difference. As applications of the post-quantum calculus known as the ( p , q ) $(
Serkan Araci +3 more
doaj +2 more sources
A note on (p,q) $(p,q)$-Bernstein polynomials and their applications based on (p,q) $(p,q)$-calculus
Journal of Inequalities and Applications, 2018 Nowadays (p,q) $(p,q)$-Bernstein polynomials have been studied in many different fields such as operator theory, CAGD, and number theory. In order to obtain the fundamental properties and results of Bernstein polynomials by using (p,q) $(p,q)$-calculus ...
Erkan Agyuz, Mehmet Acikgoz
doaj +2 more sources
A new concept of q-calculus with respect to another function [PDF]
Journal of Innovative Applied Mathematics and Computational SciencesIn this paper, we present an approach to quantum calculus and its applications through a functional method. This approach enables the exploration of the number-theoretic properties of q-calculus in a functional framework, facilitating the modification ...
Shrinath Manjarekar, Hossein Jafari
doaj +2 more sources
On the solutions of some fractional q-differential equations with the Riemann-Liouville fractional q-derivative [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2021 This paper is devoted to explicit and numerical solutions to linear fractional q-difference equations and the Cauchy type problem associated with the Riemann-Liouville fractional q-derivative in q-calculus.
S. Shaimardan, N.S. Tokmagambetov
doaj +3 more sources
The Schr¨odinger equations generated by q-Bessel operator in quantum calculus [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2022 In this paper, we obtain exact solutions of a new modification of the Schrödinger equation related to the Bessel q -operator. The theorem is proved on the existence of this solution in the Sobolev-type space Wq2(R+q ) in the q -calculus.
S. Shaimardan, N.S. Tokmagambetov
doaj +2 more sources
Wirtinger type q-integral inequalities on q-calculus [PDF]
, 2021 In this study, we obtained two kinds of Wirtinger type q-inequalities on quantum calculus. Then, we proved a more general Wirtinger type q-integral inequality. With all these, we obtained classical results for q -> 1(-)
Necmettin Alp, Alp, Necmettin
core +1 more source