scholarly journals Approximate controllability of impulsive partial neutral stochastic functional integro-differential inclusions with infinite delay

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Zuomao Yan ◽  
Fangxia Lu
Keyword(s):  
Differential Inclusions ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Stochastic Functional

Approximate Controllability of Partial Fractional Neutral Integro-Differential Inclusions With Infinite Delay in Hilbert Spaces

2016 ◽  
Vol 11 (1) ◽  
Author(s):  
Zuomao Yan ◽  
Hongwu Zhang
Keyword(s):  
Hilbert Spaces ◽  
Differential Inclusions ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Multivalued Operators ◽  
Approximately Controllable ◽  
Fractional System ◽  
The Fixed Point Theorem ◽  
Necessary And Sufficient

We study the approximate controllability of a class of fractional partial neutral integro-differential inclusions with infinite delay in Hilbert spaces. By using the analytic α-resolvent operator and the fixed point theorem for discontinuous multivalued operators due to Dhage, a new set of necessary and sufficient conditions are formulated which guarantee the approximate controllability of the nonlinear fractional system. The results are obtained under the assumption that the associated linear system is approximately controllable. An example is provided to illustrate the main results.

scholarly journals On Approximate Controllability of Second-Order Neutral Partial Stochastic Functional Integrodifferential Inclusions with Infinite Delay and Impulsive Effects

2015 ◽  
Vol 2015 ◽  
pp. 1-26 ◽  
Author(s):  
Zuomao Yan
Keyword(s):  
Stochastic Analysis ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Operators ◽  
Bounded Linear ◽  
Approximation Techniques ◽  
Approximately Controllable ◽  
Stochastic Functional

We discuss the approximate controllability of second-order impulsive neutral partial stochastic functional integrodifferential inclusions with infinite delay under the assumptions that the corresponding linear system is approximately controllable. Using the fixed point strategy, stochastic analysis, and properties of the cosine family of bounded linear operators combined with approximation techniques, a new set of sufficient conditions for approximate controllability of the second-order impulsive partial stochastic integrodifferential systems are formulated and proved. The results in this paper are generalization and continuation of the recent results on this issue. An example is provided to show the application of our result.

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