scholarly journals PSEUDO ALMOST PERIODIC IN DISTRIBUTION SOLUTIONS AND OPTIMAL SOLUTIONS TO IMPULSIVE PARTIAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

2018 ◽  
Vol 8 (5) ◽  
pp. 1396-1440
Author(s):  
Zuomao Yan ◽  
◽  
Xiumei Jia
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Infinite Delay ◽  
Optimal Solutions ◽  
Almost Periodic ◽  
Pseudo Almost Periodic

Existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay

2019 ◽  
Vol 20 (01) ◽  
pp. 2050003
Author(s):  
Xiao Ma ◽  
Xiao-Bao Shu ◽  
Jianzhong Mao
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Stochastic Differential Equations ◽  
Periodic Solutions ◽  
Infinite Delay ◽  
Almost Periodic Solutions ◽  
Almost Periodic

In this paper, we investigate the existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay in Hilbert space. The main conclusion is obtained by using fractional calculus, operator semigroup and fixed point theorem. In the end, we give an example to illustrate our main results.

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