Related papers: Differential equations for Changhee polynomials an…
In this paper, we established some integral formulas for and involving the noncentral Tanny-Dowling polynomials. These formulas are shown to be generalizations of some known results on the classical geometric polynomials.
In this paper, we consider central complete and incomplete Bell polynomials which are generalizations of the recently introduced central Bell polynomials and central analogues for the complete and incomplete Bell polynomials. We investigate…
A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.
We obtain novel nonlinear Schr\"{o}dinger-Pauli equations through a formal non-relativistic limit of appropriately constructed nonlinear Dirac equations. This procedure automatically provides a physical regularisation of potential…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
In this study linear and nonlinear higher order singularly perturbed problems are examined by a numerical approach, the differential quadrature method. Here, the main idea is using Chebyshev polynomials to acquire the weighting coefficient…
We study, in this paper, a one parameter deformation of the $q-$Laguerre weight function. An investigation is made on the polynomials orthogonal with respect to such a weight. With the aid of the two compatibility conditions previously…
We derive certain systems of differential equations for matrix elements of products and iterates of logarithmic intertwining operators among strongly graded generalized modules for a strongly graded conformal vertex algebra under suitable…
We study Heun's differential equation in the case that one of the singularities is apparent. In particular we conjecture a relationship with generalized hypergeometric differential equation and establish it in some cases. We apply our…
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…
In this paper, we introduce two new non-singular kernel fractional derivatives and present a class of other fractional derivatives derived from the new formulations. We present some important results of uniformly convergent sequences of…
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…
An alternative derivation is presented of the infinitely many exceptional Wilson and Askey-Wilson polynomials, which were introduced by the present authors in 2009. Darboux-Crum transformations intertwining the discrete quantum mechanical…
Difference equations have many applications and play an important role in numerical analysis, probability, statistics, combinatorics, computer science, quantum consciousness, etc. We first prove that the partial differential equation is…
The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials…
The expressions of solutions for general $n\times m$ matrix-valued inhomogeneous linear stochastic differential equations are derived. This generalizes a result of Jaschke (2003) for scalar inhomogeneous linear stochastic differential…
In the present article, we study Bell based Euler polynomial of order {\alpha} and investigate some useful correlation formula, summation formula and derivative formula. Also, we introduce some relation of string number of the second kind.…
Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations. These lectures give a review of these developments, while not assuming any prior knowledge of the…
Time-dependent Partial Differential Equations with given initial conditions are considered in this paper. New differentiation techniques of the unknown solution with respect to time variable are proposed. It is shown that the proposed…
The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they have to fulfill certain conditions to…