Related papers: Differential equations for Changhee polynomials an…
In this paper we solve some differential equations in the $D_h$ derivative in Ward's sense. We use a special metric in the formal power series ring $\K[[x]]$. The solutions of that equations are giving in terms of fixed points for certain…
We prove some uniqueness results which improve and generalize results of Jiang-Tao Li and Ping Li[Uniqueness of entire functions concerning differential polynomials. Commun. Korean Math. Soc. 30 (2015), No. 2, pp. 93-101].
Some differential equations are considered in the context of Synthetic Differential Geometry. Here, this means that not only nilpotent infinitesimals, but also the formation of function spaces, is exploited. In particular, we utilize…
In the present paper, we investigate some interesting properties including several special polynomials arising from Caputo-fractional derivative. From our investigation, we derive a lot of interesting identities of several special…
In this paper we discuss a framework for the polynomial approximation to the solution of initial value problems for differential equations. The framework, initially devised for the approximation of ordinary differential equations, is…
In this paper, we study degenerate ordered Bell polynomials with the viewpoint of Carlitz's degenerate Bernoulli and Euler polynomials and derive by using umbral calculus some properties and new identities for the degenerate ordered Bell…
In this short note we discuss ordinary differential equations which linearize upon one (or more) differentiations. Although the subject is fairly elementary, equations of this type arise naturally in the context of integrable systems.
The aim of this paper is twofold. The first one is to find several relations between the type 2 higher-order degenerate Euler polynomials and the type 2 higher-order Changhee polynomials in connection with the degenerate stirling numbers of…
Many mathematicians have been studying various degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. Our main focus here is a new type of degenerate poly-Euler polynomials and numbers. This…
We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the…
In this paper we presents an algorithm for finding a solution of the linear nonhomogeneous quaternionic-valued differential equations. Moveover, several examples shows the feasibility of our algorithm.
We study equations with infinitely many derivatives. Equations of this type form a new class of equations in mathematical physics. These equations originally appeared in p-adic and later in fermionic string theories and their investigation…
Algorithms and underlying mathematics are presented for numerical computation with periodic functions via approximations to machine precision by trigonometric polynomials, including the solution of linear and nonlinear periodic ordinary…
Differential systems with a Fuchsian linear part are studied in regions including all the singularities in the complex plane of these equations. Such systems are not necessarily analytically equivalent to their linear part (they are not…
Differential calculus on the quantum quaternionic group GL(1,H$_q$) is introduced.
We consider semiclassical orthogonal polynomials on the unit circle associated with a weight function that satisfy a Pearson-type differential equation involving two polynomials of degree at most three. Structure relations and difference…
In the paper, we investigate the uniqueness problem of entire functions concerning their linear differential polynomial in shift and obtain three results which improve and generalize the recent result due to Qi (Ann. Polon. Math., 102…
Recently, Kim-Kim introduced the lambda-umbral calculus, in which the lambda-Sheffer sequences occupy the central position. In this paper, we introduce the fully degenerate Bell and the fully degenerate Dowling polynomials, and investigate…
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…
The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere. First, we will get connection formulas relating classical…