Related papers: Noncommutative Partial Derivative
Sequences of actions do not commute.. For example, the tick of a clock and the measurement of a position do not commute with one another, since the position will have moved to the next position after the tick. We adopt non-commutative…
In this article, we introduce a new general definition of fractional derivative and fractional integral, which depends on an unknown kernel. By using these definitions, we obtain the basic properties of fractional integral and fractional…
Non-point invertible transformations are completely described for difference equations on the quad-graph and for their differential-difference analogues. As an illustration, these transformations are used to construct new examples of…
We discuss the noncommutative generalizations of polynomial algebras which after appropriate completions can be used as coordinate algebras in various noncommutative settings, (noncommutative differential geometry, noncommutative algebraic…
We define the tangential derivative, a notion of directional derivative which is invariant under diffeomorphisms. In particular this derivative is invariant under changes of chart and is thus well-defined for functions defined on a…
We consider a nonlinear parabolic equation of fractional order in space and propose its numerical discretization. The fractional derivative is defined through a functional analytic setting, rather than the traditional definition of…
We discuss the application of variational methods, based on non-smooth critical point theory, to a general class of partial differential inclusions.
This paper introduces a notion of integrality that is suitable for non-commutative varieties. It is compatible with the usual notion of integrality for schemes. The function field and generic point of a non-commutative integral space are…
There are many possible definitions of derivatives, here we present some and present one that we have called generalized that allows us to put some of the others as a particular case of this but, what interests us is to determine that there…
This paper presents some sufficient conditions for the existence of solutions of fractional differential equation with nonlocal multi-point boundary conditions involving Caputo fractional derivative and integral boundary conditions. Our…
In this paper, we introduce a new generalized derivative, which we term the specular derivative. We establish the Quasi-Rolles' Theorem, the Quasi-Mean Value Theorem, and the Fundamental Theorem of Calculus in light of the specular…
Let C be an algebraically closed field and X a projective curve over C. Consider an ordinary linear differential equation, or a linear differ- ence equation, with coefficients in the field of rational functions of X, and assume that its…
In this paper, we propose a new concept of derivative with respect to an arbitrary kernel-function. Several properties related to this new operator, like inversion rules, integration by parts, etc. are studied. In particular, we introduce…
New techniques for evaluating the closed time path action for non-equilibrium quantum fields are presented. A derivative expansion is performed using a proper time kernel. Applications relevant to the scalar field theory of warm inflation…
We extend the usual definition of the derivative in a way that Calculus I students can easily comprehend and which allows calculations at branch points.
We introduce the notion of a combinatorial inverse system in non-commutative variables. We present two important examples, some conjectures and results. These conjectures and results were suggested and supported by computer investigations.
The central structure in various versions of noncommutative geometry is a differential calculus on an associative algebra. This is an analogue of the calculus of differential forms on a manifold. In this short review we collect examples of…
Leibniz's rule for the $n$-th derivative of a product is a very well known and extremely useful formula. In this article, we introduce an analogous explicit formula for the $n$-th derivative of a quotient of two functions. Later, we use…
Quantum Euclidean spaces, as Moyal deformations of Euclidean spaces, are the model examples of noncompact noncommutative manifold. In this paper, we study the quantum Euclidean space equipped with partial derivatives satisfying canonical…
Various kinds of infinitary operations satisfying forms of associativity have been considered in the literature by various authors, including A. Tarski, C. Karp, J. H. Conway, D. Krob, N. Bedon, and C. Rispal. Applications include the…