S-Asymptotically Periodic Solutions for Time-Space Fractional Evolution Equation

2021 ◽  
Vol 18 (4) ◽  
Author(s):  
Qiang Li ◽  
Lishan Liu ◽  
Mei Wei
Keyword(s):  
Evolution Equation ◽  
Periodic Solutions ◽  
Fractional Evolution Equation ◽  
Time Space ◽  
Asymptotically Periodic ◽  
Asymptotically Periodic Solutions

scholarly journals Existence and Global Asymptotic Behavior of S -Asymptotically ω -Periodic Solutions for Evolution Equation with Delay

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Hong Qiao ◽  
Qiang Li ◽  
Tianjiao Yuan
Keyword(s):  
Asymptotic Behavior ◽  
Evolution Equation ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Compact Semigroup ◽  
Existence Results ◽  
Asymptotically Periodic ◽  
Abstract Evolution Equation ◽  
Equation With Delay ◽  
Asymptotically Periodic Solutions

This paper is concerned with the abstract evolution equation with delay. Firstly, we establish some sufficient conditions to ensure the existence results for the S -asymptotically periodic solutions by means of the compact semigroup. Secondly, we consider the global asymptotic behavior of the delayed evolution equation by using the Gronwall-Bellman integral inequality involving delay. These results improve and generalize the recent conclusions on this topic. Finally, we give an example to exhibit the practicability of our abstract results.

scholarly journals Existence of asymptotically periodic solutions for semilinear evolution equations with nonlocal initial conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 792-805
Author(s):  
Junfei Cao ◽  
Zaitang Huang
Keyword(s):  
Periodic Solutions ◽  
Evolution Equations ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Nonlocal Initial Conditions ◽  
Asymptotically Periodic ◽  
Semilinear Evolution Equations ◽  
Asymptotically Periodic Solutions

AbstractIn this paper we study a class of semilinear evolution equations with nonlocal initial conditions and give some new results on the existence of asymptotically periodic mild solutions. As one would expect, the results presented here would generalize and improve some results in this area.

scholarly journals Existence and Stability of Square-Mean S-Asymptotically Periodic Solutions to a Fractional Stochastic Diffusion Equation with Fractional Brownian Motion

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Jia Mu ◽  
Jiecuo Nan ◽  
Yong Zhou
Keyword(s):  
Brownian Motion ◽  
Diffusion Equation ◽  
Periodic Solutions ◽  
Fractional Brownian Motion ◽  
Stochastic Diffusion ◽  
Stochastic Diffusion Equation ◽  
Asymptotically Periodic ◽  
Existence And Stability ◽  
The Fixed Point Theorem ◽  
Asymptotically Periodic Solutions

In this paper, a generalized Gronwall inequality is demonstrated, playing an important role in the study of fractional differential equations. In addition, with the fixed-point theorem and the properties of Mittag–Leffler functions, some results of the existence as well as asymptotic stability of square-mean S-asymptotically periodic solutions to a fractional stochastic diffusion equation with fractional Brownian motion are obtained. In the end, an example of numerical simulation is given to illustrate the effectiveness of our theory results.

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