Asymptotically Almost Automorphic Solution for Neutral Functional Integro Evolution Equations on Time Scales

2019 ◽  
pp. 113-127
Author(s):  
Soniya Dhama ◽  
Syed Abbas
Keyword(s):  
Time Scales ◽  
Evolution Equations ◽  
Almost Automorphic

scholarly journals S-Almost Automorphic Solutions for Impulsive Evolution Equations on Time Scales in Shift Operators

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1028
Author(s):  
Chao Wang ◽  
Rathinasamy Sakthivel ◽  
Gaston M. N’Guérékata
Keyword(s):  
Time Scales ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Dynamic Equations ◽  
Shift Operators ◽  
Almost Automorphic ◽  
Almost Automorphic Functions ◽  
New Concepts ◽  
Impulsive Evolution Equations ◽  
Automorphic Functions

In this paper, based on the concept of complete-closed time scales attached with shift direction under non-translational shifts (or S-CCTS for short), as a first attempt, we develop the concepts of S-equipotentially almost automorphic sequences, discontinuous S-almost automorphic functions and weighted piecewise pseudo S-almost automorphic functions. More precisely, some novel results about their basic properties and some related theorems are obtained. Then, we apply the introduced new concepts to investigate the existence of weighted piecewise pseudo S-almost automorphic mild solutions for the impulsive evolution equations on irregular hybrid domains. The obtained results are valid for q-difference partial dynamic equations and can also be extended to other dynamic equations on more general time scales. Finally, some heat dynamic equations on various hybrid domains are provided as applications to illustrate the obtained theory.

scholarly journals On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Jing Cui ◽  
Litan Yan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Banach Fixed Point Theorem ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Almost Automorphic ◽  
Composition Theorem

We consider a class of nonautonomous stochastic evolution equations in real separable Hilbert spaces. We establish a new composition theorem for square-mean almost automorphic functions under non-Lipschitz conditions. We apply this new composition theorem as well as intermediate space techniques, Krasnoselskii fixed point theorem, and Banach fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions. Some known results are generalized and improved.

Almost Automorphic Dynamic Equations on Translation Time Scales

2020 ◽  
pp. 477-504
Author(s):  
Chao Wang ◽  
Ravi P. Agarwal ◽  
Donal O’Regan ◽  
Rathinasamy Sakthivel
Keyword(s):  
Time Scales ◽  
Dynamic Equations ◽  
Almost Automorphic
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