time-scales
Aumann Integral on Time Scales
... In this paper, we consider by the first time the Aumann integral on time scales. Hence, we introduce the Aumann ∆-integral on time scales. We also have established properties for the ...
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Periodic boundary value problems on time scales
... all time scales, but for the existence of monotone sequences we use the Lipschitz condition with the constant which depends on the supremum of the graininess function of a particular time scale (see ...
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Some dynamic inequalities on time scales and their applications
... on time scales, which extend some known retarded dynamic inequalities on time scales, also unify and extend some continuous inequalities and their corresponding discrete analogues in the ...
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Asymptotic stability for dynamic equations on time scales
... Exponential decay and stability of solutions of dynamic equations on time scales were investigated in recent papers [1, 5–7, 11, 12] using Lyapunov’s method. We use different approaches based on integral ...
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Boundedness in functional dynamic equations on time scales
... In this section, we introduce a calculus on time scales including preliminary results. An introduction with applications and advances in dynamic equations are given in [2, 3]. Our aim is not only to unify ...
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Stability of Linear Dynamic Systems on Time Scales
... Remark 3.16. P ¨otzsche et al. 12 proved a necessary and sufficient condition for the exponential stability of time-variant linear systems on time scales in terms of the eigenvalues of the system ...
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Stability of abstract dynamic equations on time scales
... on time scales was introduced by Stefan Hilger in [], in order to unify continuous and discrete calculus [, ...A time scale T is a nonempty closed subset of R ...A time scale T is said ...
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Exponential stability of dynamic equations on time scales
... we use Lyapunov-type functions on time scales and then formulate appropriate inequal- ities on these functions that guarantee that the trivial solution to (1.1) is exponentially or uniformly exponentially ...
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Study of nonlinear Pachpatte’s inequalities on time scales
... The setup of this paper is as follows: Sect. 2 is confined to the basic definitions and pre- liminary results of calculus on time scales (for further understanding, see [3, 4], and [5]). In Sect. 3 a ...
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On transport phenomena and equilibration time scales in thermodenuders
... residence time available in the TD, oth- erwise volatility would be underestimated (An et ...idence time in a typical TD is sufficient for equilibration at the experimental conditions of their study ...
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Variationally stable dynamic systems on time scales
... In this paper we give a Lyapunov functional characterization of h-stability for nonlinear dynamic systems on time scales under the condition of u ∞ -similarity between their variational systems. ...
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Changing periodic time scales and decomposition theorems of time scales with applications to functions with local almost periodicity and automorphy
... of time scales which provides bridges between periodic time scales and an arbitrary time scale with a bounded graininess function μ ...changing-periodic time scales and ...
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On Some Integral Inequalities on Time Scales and Their Applications
... The theory of time scales was introduced by Hilger 1 in 1988 in order to contain both difference and differential calculus in a consistent way. Recently, many authors have extended some fundamental integral ...
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Bounds of Certain Dynamic Inequalities on Time Scales
... Abstract. In this paper we study explicit bounds of certain dynamic integral inequalities on time scales. These estimates give the bounds on unknown functions which can be used in studying the qualitative ...
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Uniform Lacunary Statistical Convergence on Time Scales
... The measure theory on time scales was first constructed by Guseinov [19] and Lebesque ∆-integral on time scales introduced by Cabada and Vivero [6]. Now, we introduce m-uniform strongly p- ...
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Dynamic integral inequalities on time scales with ‘maxima’
... To the best of our knowledge, there are not papers in the literature dealing with inequal- ities on time scales with ‘maxima’. To fill this gap, we initiate in this paper the study of inte- gral inequalities ...
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Nonlinear integral inequalities on time scales with ‘maxima’
... In this paper we continue the study of [] and investigate some nonlinear dynamic integral inequalities on time scales with ‘maxima’. This paper is organized as follows. In Section we give some ...
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Some Nonlinear Integral Inequalities on Time Scales
... Remark 3.17. Using our main results in this paper, we can obtain many dynamic inequal- ities on some peculiar time scales. Due to limited space, their statements are omitted here. At the end of this paper, ...
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Some complements of Cauchy's inequality on time scales
... a time scale and developed the calculus for functions on a time scale ...on time scales, which extend some results of Cargo [6], Diaz, Goldman, and Metcalf [7–11], Goldman [12], Greub and ...
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Oceanic tracer and proxy time scales revisited
... different time-dependent signal farther ...and time scales necessary to produce step- or pulse-like behavior, thus trans- forming abrupt shifts, usually on short spatial scales, into much more ...
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