Almost Automorphic Functions and Generalizations on Translation Time Scales

2020 ◽  
pp. 283-336
Author(s):  
Chao Wang ◽  
Ravi P. Agarwal ◽  
Donal O’Regan ◽  
Rathinasamy Sakthivel
Keyword(s):  
Time Scales ◽  
Almost Automorphic ◽  
Almost Automorphic Functions ◽  
Automorphic Functions

Weighted pseudo δ-almost automorphic functions and abstract dynamic equations

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Chao Wang ◽  
Ravi P. Agarwal ◽  
Donal O’Regan
Keyword(s):  
Time Scales ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Automorphic Function ◽  
Dynamic Equations ◽  
Almost Automorphic ◽  
Almost Automorphic Function ◽  
Almost Automorphic Functions ◽  
Automorphic Functions

Abstract In this paper, we propose the concept of a weighted pseudo δ-almost automorphic function under the matched space for time scales and we present some properties. Also, we obtain sufficient conditions for the existence of weighted pseudo δ-almost automorphic mild solutions to a class of semilinear dynamic equations under the matched spaces for time scales.

scholarly journals Almost Automorphic Functions of Ordernand Applications to Dynamic Equations on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Gisèle Mophou ◽  
Gaston Mandata N’Guérékata ◽  
Aril Milce
Keyword(s):  
Time Scales ◽  
Existence And Uniqueness ◽  
Dynamical Equation ◽  
Time Varying ◽  
First Order ◽  
Time Varying Delay ◽  
Almost Automorphic ◽  
Almost Automorphic Functions ◽  
Varying Delay ◽  
Automorphic Functions

We revisit the notion on almost automorphic functions on time scales given by Lizama and Mesquita (2013). Then we present the notion of almost automorphic functions of ordern. Finally, we apply this notion to study the existence and uniqueness and the global stability of almost automorphic solution of first order to a dynamical equation with finite time varying delay.

scholarly journals n0-Order Weighted Pseudo Δ-Almost Automorphic Functions and Abstract Dynamic Equations

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 775 ◽  
Author(s):  
Wang ◽  
Agarwal ◽  
O’Regan ◽  
N’Guérékata
Keyword(s):  
Time Scales ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Automorphic Function ◽  
Dynamic Equations ◽  
Open Problems ◽  
Almost Automorphic ◽  
Almost Automorphic Function ◽  
Almost Automorphic Functions ◽  
Automorphic Functions

In this paper, we introduce the concept of a n 0 -order weighted pseudo Δ n 0 δ -almost automorphic function under the matched space for time scales and we present some properties. The results are valid for q-difference dynamic equations among others. Moreover, we obtain some sufficient conditions for the existence of weighted pseudo Δ n 0 δ -almost automorphic mild solutions to a class of semilinear dynamic equations under the matched space. Finally, we end the paper with a further discussion and some open problems of this topic.

scholarly journals Bochner definition of Stepanov-like almost automorphic functions on time scales and an application to cellular neural networks with delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Li-Li Zhang ◽  
Xu-Dong Yang
Keyword(s):  
Neural Networks ◽  
Time Scales ◽  
Dynamic Equation ◽  
Cellular Neural Networks ◽  
Automorphic Function ◽  
Almost Automorphic ◽  
Almost Automorphic Function ◽  
Almost Automorphic Functions ◽  
Definition Of ◽  
Automorphic Functions

AbstractThe definition of Stepanov-like almost automorphic functions on time scales had been proposed in the literature, but at least one result was incorrect, which involved Bochner transform. In our work, we give the Bochner definition of Stepanov-like almost automorphic functions on time scales, and prove that a function is Stepanov-like almost automorphic if and only if it satisfies Bochner definition of Stepanov-like almost automorphic function on time scales. The Bochner definition of Stepanov-like almost automorphic functions on time scales corrects the faulty result, and perfects the definition of Stepanov-like almost automorphic functions. As applications, we discuss the almost automorphy of a certain dynamic equation and some cellular neural networks with delays on time scales.

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