Periodicity, almost periodicity for time scales
and related functions

Wang, Chao; Agarwal, Ravi P.; O’Regan, Donal

doi:10.1515/msds-2016-0003

Cited by 30 publications

(51 citation statements)

References 12 publications

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“…Since Π * * is relatively dense in Π in Definition 2.9, one can observe that the graininess function µ is bounded. From [33], we can see that ACCTS is the most general type of independent variables with almost periodicity.…”

Section: Introductionmentioning

confidence: 93%

“…The theory of dynamic equations on time scales also extends to cases "in between", e.g., to the so-called q-difference equations (T = q N 0 := {q t : t ∈ N 0 for q > 1}) or (T = q Z := q Z ∪ {0}), and can be applied on different types of time scales such as T = hN, T = N 2 , and T = T n the space of the harmonic numbers. Several authors have expounded on various aspects of this new theory (see [1,2,4,7,18,33]). …”

Section: Introductionmentioning

confidence: 99%

“…Time scales hZ and R have some very nice properties so that the dynamic change of functions established on them can be described well because of the closedness for the translation of time variables. All periodic time scales have a nice closedness for the translation of time variables (see [20,33]), and we say T is with "complete closedness" (CCTS). A time scale with such a type of "complete closedness" assists in conquering the difficulties of defining and studying functions on time scales.…”

Section: Introductionmentioning

confidence: 99%

“…If ±τ ∈ E{T, ε 1 } in Definition 2.6 from [33], then there exists A 1 , which implies that almost periodic time scales introduced in [30,31] are bi-direction ACCTS with inf T = −∞, sup T = +∞. For more important comments and remarks of almost periodic time scales, one may consult [3,33].…”

Section: Introductionmentioning

confidence: 99%

“…Since the concept of almost periodic time scales from [33] is a particular case of Definition 2.6, if T is a bi-direction ACCTS (i.e., an almost periodic time scale), then…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Weighted piecewise pseudo double-almost periodic solution for impulsive evolution equations

Wang¹,

Agarwal²,

O’Regan³

2017

J. Nonlinear Sci. Appl.

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In this paper, based on the concept and properties of almost-complete closedness time scales (ACCTS), we investigate the existence of weighted pseudo double-almost periodic mild solutions for non-autonomous impulsive evolution equations. We also consider the exponential stability of weighted pseudo double-almost periodic solutions. Finally, we conclude our paper by providing several illustrative applications to different types of dynamic equations and mathematical models. These applications justify the practical usefulness of the established theoretical results.

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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Since the concept of almost periodic time scales from [33] is a particular case of Definition 2.6, if T is a bi-direction ACCTS (i.e., an almost periodic time scale), then…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Weighted piecewise pseudo double-almost periodic solution for impulsive evolution equations

Wang¹,

Agarwal²,

O’Regan³

2017

J. Nonlinear Sci. Appl.

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Delay dynamic equations on isolated time scales and the relevance of one‐periodic coefficients

Böhner

Cuchta

Streipert

2022

Math Methods in App Sciences

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We are motivated by the idea that certain properties of delay differential and difference equations with constant coefficients arise as a consequence of their one-periodic nature. We apply the recently introduced definition of periodicity for arbitrary isolated time scales to linear delay dynamic equations and a class of nonlinear delay dynamic equations. Utilizing a derived identity of higher order delta derivatives and delay terms, we rewrite the considered linear and nonlinear delayed dynamic equations with one-periodic coefficients as a linear autonomous dynamic system with constant matrix. As the simplification of a constant matrix is only obtained for one-periodic coefficients, dynamic equations with one-periodic coefficients are the simplest form compared to the commonly used constant coefficients.

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Almost periodic fractional fuzzy dynamic equations on timescales: A survey

Wang,

Tan,

Agarwal

2023

Math Methods in App Sciences

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In this paper, we systematically present some main results of the fractional calculus, almost periodic functions, fuzzy functions, fuzzy fractional calculus, and almost periodic generalized fuzzy dynamic equations on timescales. Moreover, the potential future research of almost periodic fractional fuzzy dynamic equations on timescales is discussed. The results presented in this survey can be applied to study the qualitative theory of almost periodic fractional fuzzy dynamic equations and fuzzy fractional calculus on timescales.

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Periodicity, almost periodicity for time scales and related functions

Cited by 30 publications

References 12 publications

Weighted piecewise pseudo double-almost periodic solution for impulsive evolution equations

Weighted piecewise pseudo double-almost periodic solution for impulsive evolution equations

Delay dynamic equations on isolated time scales and the relevance of one‐periodic coefficients

Almost periodic fractional fuzzy dynamic equations on timescales: A survey

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