scholarly journals Uncertain fractional forward difference equations for Riemann–Liouville type

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Qinyun Lu ◽  
Yuanguo Zhu ◽  
Ziqiang Lu
Keyword(s):  
Difference Equations ◽  
Liouville Type ◽  
Forward Difference

On the spectral analysis of self adjoint operators generated by second order difference equations

1991 ◽  
Vol 118 (1-2) ◽  
pp. 139-151 ◽  
Author(s):  
Dale T. Smith
Keyword(s):  
Essential Spectrum ◽  
Difference Equations ◽  
Difference Operator ◽  
Simple Criterion ◽  
Order Difference ◽  
Forward Difference ◽  
Other Information ◽  
Image Position ◽  
Adjoint Operators ◽  
Oscillation Constant

SynopsisIn this paper, I shall consider operators generated by difference equations of the formwhere Δ is the forward difference operator, and a, p, and r are sequences of real numbers. The connection between the oscillation constant of this equation and the bottom of the essential spectrum of self-adjoint extensions of the operator generated by the equation is given, as well as various other information about the spectrum of such extensions. In particular, I derive conditions for the spectrum to have only countably many eigenvalues below zero, and a simple criterion for the invariance of the essential spectrum.

scholarly journals A Correlation Between Solutions of Uncertain Fractional Forward Difference Equations and Their Paths

2020 ◽  
Vol 8 ◽  
Author(s):  
Hari Mohan Srivastava ◽  
Pshtiwan Othman Mohammed
Keyword(s):  
Fractional Calculus ◽  
Uniqueness Theorem ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Comparison Theorems ◽  
Existence And Uniqueness Theorem ◽  
Discrete Fractional Calculus ◽  
Uncertain Variables ◽  
Forward Difference ◽  
The Relationship

We consider the comparison theorems for the fractional forward h-difference equations in the context of discrete fractional calculus. Moreover, we consider the existence and uniqueness theorem for the uncertain fractional forward h-difference equations. After that the relations between the solutions for the uncertain fractional forward h-difference equations with symmetrical uncertain variables and their α-paths are established and verified using the comparison theorems and existence and uniqueness theorem. Finally, two examples are provided to illustrate the relationship between the solutions.

Asymptotic behavior in neutral difference equations with negative coefficients

2014 ◽  
Vol 64 (2) ◽  
Author(s):  
G. Chatzarakis ◽  
G. Miliaras
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equation ◽  
Difference Equations ◽  
Difference Operator ◽  
Retarded Argument ◽  
Real Numbers ◽  
Neutral Difference Equation ◽  
Neutral Difference Equations ◽  
Forward Difference ◽  
Deviated Argument

AbstractIn this paper, we study the asymptotic behavior of the solutions of a neutral difference equation of the form $\Delta [x(n) + cx(\tau (n))] - p(n)x)(\sigma (n)) = 0,$, where τ(n) is a general retarded argument, σ(n) is a general deviated argument, c ∈ ℝ, (−p(n))n≥0 is a sequence of negative real numbers such that p(n) ≥ p, p ∈ ℝ+, and Δ denotes the forward difference operator Δx(n) = x(n+1)−x(n).

scholarly journals Oscillation for Super Linear/Linear Second Order Neutral Difference Equations with Variable Several Delays

2020 ◽  
Vol 5 (4) ◽  
pp. 663-681
Author(s):  
Chittaranjan Behera ◽  
Radhanath Rath ◽  
Prayag Prasad Mishra
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Difference Operator ◽  
Sufficient Conditions ◽  
Second Order ◽  
Multiple Delays ◽  
Neutral Difference Equation ◽  
Neutral Difference Equations ◽  
Forward Difference ◽  
Several Delays

This article, is concerned with finding sufficient conditions for the oscillation and non oscillation of the solutions of a second order neutral difference equation with multiple delays under the forward difference operator, which generalize and extend some existing results.This could be possible by extending an important lemma from the literature.

scholarly journals Oscillation criteria for certain second order nonlinear difference equations

1999 ◽  
Vol 60 (1) ◽  
pp. 95-108 ◽  
Author(s):  
S.R. Grace ◽  
H.A. El-Morshedy
Keyword(s):  
Difference Equations ◽  
Difference Operator ◽  
Nonnegative Function ◽  
Second Order ◽  
Real Sequence ◽  
Nonlinear Difference Equations ◽  
Oscillation Criteria ◽  
Forward Difference ◽  
Image Position

This paper is concerned with nonlinear difference equations of the formwhere δ is the forward difference operator defined by δun−1 = un − un −1 δ2un −1= δ(δun-1) and {an} is a real sequence which is not assumed to be nonnegative. The function f is such that uf(u) < 0 for all u ≠ 0 and f(u) − f(v) = g(u, v)(u − v), for all u, v ≠ 0, and for some nonnegative function g. Our results are not only new but also improve and generalise some recent oscillation criteria. Examples illustrating the importance of our main results are also given.

scholarly journals Meromorphic solutions of certain nonlinear difference equations

2020 ◽  
Vol 18 (1) ◽  
pp. 1292-1301
Author(s):  
Huifang Liu ◽  
Zhiqiang Mao ◽  
Dan Zheng
Keyword(s):  
Difference Equation ◽  
Finite Order ◽  
Difference Equations ◽  
Nonlinear Difference Equation ◽  
Meromorphic Solutions ◽  
Nonlinear Difference Equations ◽  
Zero Distribution ◽  
Forward Difference

Abstract This paper focuses on finite-order meromorphic solutions of nonlinear difference equation {f}^{n}(z)+q(z){e}^{Q(z)}{\text{&#x0394;}}_{c}f(z)=p(z) , where p,q,Q are polynomials, n\ge 2 is an integer, and {\text{&#x0394;}}_{c}f is the forward difference of f. A relationship between the growth and zero distribution of these solutions is obtained. Using this relationship, we obtain the form of these solutions of the aforementioned equation. Some examples are given to illustrate our results.

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