scholarly journals Some Properties Involving q-Hermite Polynomials Arising from Differential Equations and Location of Their Zeros

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1168
Author(s):  
Cheon Seoung Ryoo ◽  
Jung Yoog Kang
Keyword(s):  
Differential Equations ◽  
Hermite Polynomials ◽  
Real Numbers ◽  
Different Types

Hermite polynomials are one of the Apell polynomials and various results were found by the researchers. Using Hermit polynomials combined with q-numbers, we derive different types of differential equations and study these equations. From these equations, we investigate some identities and properties of q-Hermite polynomials. We also find the position of the roots of these polynomials under certain conditions and their stacked structures. Furthermore, we locate the roots of various forms of q-Hermite polynomials according to the conditions of q-numbers, and look for values which have approximate roots that are real numbers.

SOME PROPERTIES OF EQUIDISTRIBUTED AND WELL DISTRIBUTED SEQUENCES

2021 ◽  
Vol 10 (9) ◽  
pp. 3175-3184
Author(s):  
Leila Miller-Van Wieren
Keyword(s):  
Real Numbers ◽  
Statistical Cluster ◽  
Different Types ◽  
Limit Points ◽  
Cluster Points

Many authors studied properties related to distribution and summability of sequences of real numbers. In these studies, different types of limit points of a sequence were introduced and studied including statistical and uniform statistical cluster points of a sequence. In this paper, we aim to prove some new results about the nature of different types of limit points, this time connected to equidistributed and well distributed sequences.

scholarly journals Hyers–Ulam stability of a coupled system of fractional differential equations of Hilfer–Hadamard type

2019 ◽  
Vol 52 (1) ◽  
pp. 283-295 ◽  
Author(s):  
Manzoor Ahmad ◽  
Akbar Zada ◽  
Jehad Alzabut
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Ulam Stability ◽  
Fractional Differential System ◽  
Different Types ◽  
Fractional Differential

AbstractIn this paper, existence and uniqueness of solution for a coupled impulsive Hilfer–Hadamard type fractional differential system are obtained by using Kransnoselskii’s fixed point theorem. Different types of Hyers–Ulam stability are also discussed.We provide an example demonstrating consistency to the theoretical findings.

scholarly journals Solving Some Differential Equations Arising in Electric Engineering Using Hermite Polynomials

2020 ◽  
Vol 12 (4) ◽  
pp. 517-523
Author(s):  
G. Singh ◽  
I. Singh
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Collocation Method ◽  
Hermite Polynomials ◽  
Electric Circuit ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Electric Engineering ◽  
Collocation Points ◽  
Linear Algebraic Equations

In this paper, a collocation method based on Hermite polynomials is presented for the numerical solution of the electric circuit equations arising in many branches of sciences and engineering. By using collocation points and Hermite polynomials, electric circuit equations are transformed into a system of linear algebraic equations with unknown Hermite coefficients. These unknown Hermite coefficients have been computed by solving such algebraic equations. To illustrate the accuracy of the proposed method some numerical examples are presented.

scholarly journals Recursive Differentiation Method for Boundary Value Problems: Application to Analysis of a Beam-Column on an Elastic Foundation

2014 ◽  
Vol 44 (2) ◽  
pp. 57-70 ◽  
Author(s):  
Mohamed Taha
Keyword(s):  
Differential Equations ◽  
Analytical Solutions ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Buckling Mode ◽  
Beam Columns ◽  
Differentiation Method ◽  
Adomian Decomposition ◽  
Different Types ◽  
Finite Domains

Abstract In the present work, the recursive differentiation method (RDM) is introduced and implemented to obtain analytical solutions for differential equations governing different types of boundary value prob- lems (BVP). Then, the method is applied to investigate the static behaviour of a beam-column resting on a two parameter foundation subjected to different types of lateral loading. The analytical solutions obtained using RDM and Adomian decomposition method (ADM) are found similar but the RDM requires less mathematical effort. It is indicated that the RDM is reliable, straightforward and efficient for investigation of BVP in finite domains. Several examples are solved to describe the method and the obtained results reveal that the method is convenient for solving linear, nonlinear and higher order ordinary differential equations. However, it is indicated that, in the case of beam-columns resting on foundations, the beam-column may be buckled in a higher mode rather than a lower one, then the critical load in that case is that accompanies the higher mode. This result is very important to avoid static instability as it is widely common that the buckling load of the first buckling mode is always the smaller one, which is true only in the case of the beam-columns without foundations.

scholarly journals Stability of observations of partial differential equations under uncertain perturbations

2017 ◽  
Vol 24 (1) ◽  
pp. 45-61 ◽  
Author(s):  
Martin Lazar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Wave Operator ◽  
System Dynamic ◽  
Schrödinger Equations ◽  
Partial Differential ◽  
Main System ◽  
Different Types ◽  
The Stability ◽  
Observability Estimates

We demonstrate the stability of observability estimates for solutions to wave and Schrödinger equations subjected to additive perturbations. This work generalises recent averaged observability/control results by allowing for systems consisting of operators of different types. We also consider the simultaneous observability problem by which one tries to estimate the energy of each component of a system under consideration. Our analysis relies on microlocal defect tools, in particular on standard H-measures when the main system dynamic is governed by the wave operator, and parabolic H-measures in the case of the Schrödinger operator.

scholarly journals Solvability and Stability of Impulsive Set Dynamic Equations on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Shihuang Hong ◽  
Jing Gao ◽  
Yingzi Peng
Keyword(s):  
Differential Equations ◽  
Time Scales ◽  
Difference Equations ◽  
Time Scale ◽  
Dynamic Equations ◽  
Stability Of Solutions ◽  
Real Numbers ◽  
Generalized Derivative ◽  
Special Cases ◽  
Existence And Stability

A class of new nonlinear impulsive set dynamic equations is considered based on a new generalized derivative of set-valued functions developed on time scales in this paper. Some novel criteria are established for the existence and stability of solutions of such model. The approaches generalize and incorporate as special cases many known results for set (or fuzzy) differential equations and difference equations when the time scale is the set of the real numbers or the integers, respectively. Finally, some examples show the applicability of our results.

scholarly journals ON I-ACCELERATION CONVERGENCE OF SEQUENCES OF FUZZY REAL NUMBERS

2012 ◽  
Vol 17 (4) ◽  
pp. 549-577 ◽  
Author(s):  
Amar Jyoti Dutta ◽  
Binod Chandra Tripathy
Keyword(s):  
Decomposition Theorem ◽  
Real Numbers ◽  
Different Types ◽  
Fuzzy Real Numbers ◽  
Convergence Of Sequences

In this article we introduce the notion of ideal acceleration convergence of sequences of fuzzy real numbers. We have proved a decomposition theorem for ideal acceleration convergence of sequences as well as for subsequence transformations and studied different types of acceleration convergence of fuzzy real valued sequence.

scholarly journals VIM for Solving the Pollution Problem of a System of Lakes

2010 ◽  
Vol 2010 ◽  
pp. 1-6 ◽  
Author(s):  
J. Biazar ◽  
M. Shahbala ◽  
H. Ebrahimi
Keyword(s):  
Differential Equations ◽  
Iteration Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Environment Monitoring ◽  
System Of Differential Equations ◽  
Variational Iteration ◽  
Pollution Problem ◽  
Adomian Decomposition ◽  
Different Types

Pollution has become a very serious threat to our environment. Monitoring pollution is the first step toward planning to save the environment. The use of differential equations of monitoring pollution has become possible. In this paper the pollution problem of three lakes with interconnecting channels has been studied. The variational iteration method has been applied to compute an approximate solution of the system of differential equations, governing on the problem. Three different types of input models: sinusoidal, impulse, and step will be considered for monitoring the pollution in the lakes. The results are compared with those obtained by Adomian decomposition method. This comparison reveals that the variational iteration method is easier to be implemented.

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