scholarly journals Approximate controllability of fractional impulsive evolution systems involving nonlocal initial conditions

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Xiaozhi Zhang ◽  
Chuanxi Zhu ◽  
Chenggui Yuan
Keyword(s):  
Approximate Controllability ◽  
Initial Conditions ◽  
Nonlocal Initial Conditions ◽  
Evolution Systems

Approximate controllability of fractional stochastic evolution equations with nonlocal conditions

2020 ◽  
Vol 21 (7-8) ◽  
pp. 829-841
Author(s):  
Yonghong Ding ◽  
Yongxiang Li
Keyword(s):  
Approximate Controllability ◽  
Evolution Equations ◽  
Initial Conditions ◽  
Nonlocal Conditions ◽  
Nonlocal Term ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Approximation Techniques ◽  
Nonlocal Initial Conditions ◽  
The Fixed Point Theorem

AbstractThis paper deals with the approximate controllability for a class of fractional stochastic evolution equations with nonlocal initial conditions in a Hilbert space. We delete the compactness condition or Lipschitz condition for nonlocal term appearing in various literatures, and only need to suppose some weak growth condition on the nonlocal term. The discussion is based on the fixed point theorem, diagonal argument and approximation techniques. In the end, an example is presented to illustrate the abstract theory.

scholarly journals On the finite approximate controllability for Hilfer fractional evolution systems with nonlocal conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 529-539
Author(s):  
Xianghu Liu
Keyword(s):  
Approximate Controllability ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Evolution System ◽  
Controlled Systems ◽  
Uniqueness Of The Solution ◽  
Fractional Evolution Systems ◽  
Evolution Systems

Abstract The aim of this study is to investigate the finite approximate controllability of certain Hilfer fractional evolution systems with nonlocal conditions. To achieve this, we first transform the mild solution of the Hilfer fractional evolution system into a fixed point problem for a condensing map. Then, by using the topological degree approach, we present sufficient conditions for the existence and uniqueness of the solution of the Hilfer fractional evolution systems. Using the variational approach, we obtain sufficient conditions for the finite approximate controllability of semilinear controlled systems. Finally, an example is provided to illustrate main 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.

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