Compact Almost Automorphic Function on Time Scales and Its Application

Exponential convergence in the mean-square sense of nonlocal stochastic almost automorphic genetic regulatory lattice networks

“…A number of processes have a certain regularity; however, they are not completely periodic. So, the study of almost periodic or automorphic sequence has been a significant and interesting topic in the field of difference equations owing to the intensive evolution of the theories of difference equations and the applications in the areas of science and engineering, please refer Li and Shen (2021), Lizama and Mesquita (2013), Aouiti et al (2021), Xu et al (2020a) and Feng and Zong (2018) for some relevant works in this field.…”

Modulo periodic Poisson stable solutions of dynamic equations on a time scale

“…In the interest of brevity, MPPS trajectories are the ones which can be decomposed as the sum of periodic and Poisson stable functions. Motivated by the importance of oscillations in real world processes [12,15,18,31,36] and various application fields of dynamic equations on time scales [23][24][25][26]32,34,35], in this study, we investigate the existence, uniqueness, and asymptotic stability of MPPS solutions in such equations. To the best of our 908 F. TOKMAK FEN, M. O. FEN knowledge this is the first time in the literature that Poisson stable as well as MPPS solutions are introduced and investigated for dynamic equations on time scales.…”

Weyl almost automorphic solutions for a class of Clifford‐valued dynamic equations with delays on time scales

“…However, in a certain sense, it is not necessary to study the existence of Weyl almost automorphic solutions of differential equations and dif-ference equations, respectively, because the study of dynamic equations on time scales can unify the study of differential equations and difference equations. [7][8][9][10][11][12][13][14] Unfortunately, there is no concept of Weyl almost automorphic functions on time scales. Therefore, it is very significant to propose a concept of Weyl almost automorphy on time scales and study the existence of Weyl almost automorphic solutions of dynamic equations on time scales.…”

“…Consequently, the results of the existence of Weyl almost automorphic solutions of differential equations are very few, and the results of the existence of Weyl almost automorphic solutions of difference equations are almost missing. However, in a certain sense, it is not necessary to study the existence of Weyl almost automorphic solutions of differential equations and difference equations, respectively, because the study of dynamic equations on time scales can unify the study of differential equations and difference equations 7–14 . Unfortunately, there is no concept of Weyl almost automorphic functions on time scales.…”