Existence and Stability of Weighted Pseudo Almost Automorphic Solution of Dynamic Equation on Time Scales with Weighted Stepanov-Like ($$S^p$$Sp) Pseudo Almost Automorphic Coefficients

2020 ◽  
Vol 19 (1) ◽  
Author(s):  
Soniya Dhama ◽  
Syed Abbas
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Almost Automorphic ◽  
Existence And Stability ◽  
Pseudo Almost Automorphic ◽  
Pseudo Almost Automorphic Solution

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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