Related papers: On a New Type $pq$-Calculus
In this work, we derive numerous identities for multivariate q-Euler polynomials by using umbral calculus.
The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations.…
An exterior derivative, inner derivation, and Lie derivative are introduced on the quantum group $GL_{q}(N)$. $SL_{q}(N)$ is then found by constructing matrices with determinant unity, and the induced calculus is found.
The main aim of the present work is to give some interesting the $q$-analogues of various $q$-recurrence relations, $q$-recursion formulas, $q$-partial derivative relations, $q$-integral representations, transformation and summation…
ZX-calculus has proved to be a useful tool for quantum technology with a wide range of successful applications. Most of these applications are of an algebraic nature. However, other tasks that involve differentiation and integration remain…
The complexes of integral forms on the quantum Euclidean group $E_q(2)$ and the quantum plane are defined and their isomorphisms with the corresponding de Rham complexes are established.
In this paper, we develop a new deformation and generalization of the Natural integral transform based on the conformable fractional $q$-derivative. We obtain transformation of some deformed functions and apply the transform for solving…
Fractional $q$-extensions of some classical $q$-orthogonal polynomials are introduced and some of the main properties of the new defined functions are given. Next, a fractional $q$-difference equation of Gauss type is introduced and solved…
We propose a type-theoretic framework for describing and proving properties of quantum computations, in particular those presented as quantum circuits. Our proposal is based on an observation that, in the polymorphic type system of Coq,…
We present a novel method to derive particular solutions for partial differential equations of the form $(\operatorname{A} + \operatorname{B})^k Q(x) = q(x)$, with $\operatorname{A}$ and $\operatorname{B}$ being linear differential…
In this paper, we study a new p-adic q-l-functions and sums of powers.
This research is aimed to give a determinantal definition for the $q$-Appell polynomials and show some classical properties as well as find some interesting properties of the mentioned polynomials in the light of the new definition.
With this paper we hope to contribute to the theory of quantales and quantale-like structures. It considers the notion of $Q$-sup-algebra and shows a representation theorem for such structures generalizing the well-known representation…
In this paper, we establish a $q$-integral formula by using the orthogonality relation, and also provide a new proof of the $q$-orthogonality relation for the continuous $q$-ultraspherical polynomials. A new $q$-beta integral with five…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
We introduce $p$-derivations and give a few basic ways in which they act like derivatives by numbers.
In this paper, we define the notions $q$-birational morphism and $q$-birational divisor and develop the theory about them. We state and prove versions of Kodaira-type vanishing theorem and Zariski decomposition theorem for $q$-birational…
By using p-adic q-integrals, we study the q-Bernoulli numbers and polynomials of higher order.
In this work we establish a theory of Calculus based on the new concept of displacement. We develop all the concepts and results necessary to go from the definition to differential equations, starting with topology and measure and moving on…
In the present article, we introduce a $(p,q)$-analogue of the poly-Euler polynomials and numbers by using the $(p,q)$-polylogarithm function. These new sequences are generalizations of the poly-Euler numbers and polynomials. We give…