scholarly journals Necessary and sufficient conditions for stability of Volterra integro-dynamic equation on time scales

2016 ◽  
pp. 21-33 ◽  
Author(s):  
Youssef N. Raffoul
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

Fundamental properties of statistical convergence and lacunary statistical convergence on time scales

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4455-4467 ◽  
Author(s):  
Ceylan Turan ◽  
Oktay Duman
Keyword(s):  
Time Scales ◽  
Statistical Convergence ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Tauberian Condition ◽  
Fundamental Properties ◽  
Lacunary Statistical Convergence ◽  
Necessary And Sufficient

In this paper, we first obtain a Tauberian condition for statistical convergence on time scales. We also find necessary and sufficient conditions for the equivalence of statistical convergence and lacunary statistical convergence on time scales. Some significant applications are also presented.

scholarly journals Characterizations of weighted dynamic Hardy-type inequalities with higher-order derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. H. Saker ◽  
R. R. Mahmoud ◽  
K. R. Abdo
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Type Inequality ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Hardy Type Inequality ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Weighted Functions ◽  
Necessary And Sufficient

AbstractIn this paper, we establish some necessary and sufficient conditions for the validity of a generalized dynamic Hardy-type inequality with higher-order derivatives with two different weighted functions on time scales. The corresponding continuous and discrete cases are captured when $\mathbb{T=R}$ T = R and $\mathbb{T=N}$ T = N , respectively. Finally, some applications to our main result are added to conclude some continuous results known in the literature and some other discrete results which are essentially new.

scholarly journals Stability Criteria for Volterra Integrodynamic System

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Nusrat Yasmin ◽  
Awais Younus ◽  
Usman Ali ◽  
Safia Mirza
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Qualitative Behavior ◽  
Lyapunov Functionals ◽  
Stability Criteria ◽  
Necessary And Sufficient

We study conditions under which the solutions of linear Volterra integrodynamic system of the formyΔt=Atyt+∫t0tKt,sysΔsare stable on certain time scales. We construct a number of Lyapunov functionals on time scales from which we obtain necessary and sufficient conditions for stability of Volterra integrodynamic system and also we prove several results concerning qualitative behavior of this system.

scholarly journals Nonoscillatory Solutions for Higher-Order Neutral Dynamic Equations on Time Scales

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
Taixiang Sun ◽  
Hongjian Xi ◽  
Xiaofeng Peng ◽  
Weiyong Yu
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Dynamic Equations ◽  
Bounded Solutions ◽  
Nonoscillatory Solutions ◽  
Neutral Dynamic Equation ◽  
Necessary And Sufficient ◽  
Neutral Dynamic Equations

We study the higher-order neutral dynamic equation{a(t)[(x(t)−p(t)x(τ(t)))Δm]α}Δ+f(t,x(δ(t)))=0fort∈[t0,∞)Tand obtain some necessary and sufficient conditions for the existence of nonoscillatory bounded solutions for this equation.

ON THE MONOTONICITY OF FLUCTUATION SPECTRA FOR THREE-STATE MARKOV PROCESSES

2007 ◽  
Vol 07 (03) ◽  
pp. L181-L192 ◽  
Author(s):  
YONG CHEN
Keyword(s):  
Time Scales ◽  
Markov Processes ◽  
Correlation Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Fluctuation Spectrum ◽  
Real Functions ◽  
Explicit Formulae ◽  
Necessary And Sufficient

Explicit formulae for correlation functions and fluctuation spectra of the irreducible three-state Markov processes are presented. The necessary and sufficient conditions of existing nonmonotonic fluctuation spectra on [0, +∞) with respect to real functions are given, which reveals that the nonequilibrium flux must be strong enough to produce a peak in the fluctuation spectrum and the monotonicity of fluctuation spectra is related to the time scales of Markov processes.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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