Results on approximate controllability results for second‐order Sobolev‐type impulsive neutral differential evolution inclusions with infinite delay

2020 ◽  
Author(s):  
V. Vijayakumar ◽  
Sumati Kumari Panda ◽  
Kottakkaran Sooppy Nisar ◽  
Haci Mehmet Baskonus
Keyword(s):  
Differential Evolution ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Second Order ◽  
Sobolev Type ◽  
Evolution Inclusions

Approximate controllability of second order nonlocal neutral differential evolution inclusions

2020 ◽  
Author(s):  
V Vijayakumar ◽  
R Udhayakumar ◽  
C Dineshkumar
Keyword(s):  
Differential Evolution ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Second Order ◽  
Impulsive Systems ◽  
Evolution Inclusions

Abstract In our manuscript, we organize a group of sufficient conditions of approximate controllability for second order nonlocal neutral differential evolution inclusions. Next, we develop the result to analyze approximate controllability of impulsive systems. Lastly, a model is presented for illustration of theory.

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.

scholarly journals A note on the approximate controllability of second-order integro-differential evolution control systems via resolvent operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Velusamy Vijayakumar ◽  
Anurag Shukla ◽  
Kottakkaran Sooppy Nisar ◽  
Wasim Jamshed ◽  
Shahram Rezapour
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Evolution ◽  
Control Systems ◽  
Approximate Controllability ◽  
Semigroup Theory ◽  
Second Order ◽  
Resolvent Operators ◽  
Gronwall’S Inequality ◽  
Evolution Control

AbstractThe approximate controllability of second-order integro-differential evolution control systems using resolvent operators is the focus of this work. We analyze approximate controllability outcomes by referring to fractional theories, resolvent operators, semigroup theory, Gronwall’s inequality, and Lipschitz condition. The article avoids the use of well-known fixed point theorem approaches. We have also included one example of theoretical consequences that has been validated.

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