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 Approximate controllability of second-order nonlocal impulsive partial functional integro-differential evolution systems in Banach spaces

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5887-5912 ◽  
Author(s):  
Mahalingam Nagaraj ◽  
Velusamy Kavitha ◽  
Dumitru Baleanu ◽  
Mani Arjunan
Keyword(s):  
Differential Evolution ◽  
Banach Spaces ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Nonlinear Alternative ◽  
Banach Contraction

This manuscript is involved with a class of second-order impulsive partial functional integro-differential evolution equations with nonlocal conditions in Banach spaces. Sufficient conditions ensuring the existence and approximate controllability of mild solutions are established. Theory of cosine family, Banach contraction principle and Leray-Schauder nonlinear alternative fixed point theorem are employed for achieving the required results. An example is analyzed to illustrate the effectiveness of the outcome.

scholarly journals Approximate controllability of second order impulsive systems with state-dependent delay in banach spaces

2019 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Soniya Singh ◽  
◽  
Sumit Arora ◽  
Manil T. Mohan ◽  
Jaydev Dabas ◽  
...  
Keyword(s):  
Banach Spaces ◽  
Approximate Controllability ◽  
Second Order ◽  
Impulsive Systems ◽  
State Dependent ◽  
State Dependent Delay

APPROXIMATE CONTROLLABILITY OF SECOND-ORDER STOCHASTIC DIFFERENTIAL EQUATIONS WITH IMPULSIVE EFFECTS

2010 ◽  
Vol 24 (14) ◽  
pp. 1559-1572 ◽  
Author(s):  
RATHINASAMY SAKTHIVEL ◽  
YONG REN ◽  
N. I. MAHMUDOV
Keyword(s):  
Biological Sciences ◽  
Differential Equations ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Impulsive Effects ◽  
Infinite Dimensional ◽  
Infinite Dimensional Dynamical Systems ◽  
Necessary And Sufficient

Many practical systems in physical and biological sciences have impulsive dynamical behaviors during the evolution process which can be modeled by impulsive differential equations. In this paper, the approximate controllability of nonlinear second-order stochastic infinite-dimensional dynamical systems with impulsive effects is considered. By using the Holder's inequality, stochastic analysis and fixed point strategy, a new set of necessary and sufficient conditions are formulated which guarantees the approximate controllability of the nonlinear second-order stochastic system. The results are obtained under the assumption that the associated linear system is approximately controllable.

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.

scholarly journals On oscillatory second order nonlinear impulsive systems of neutral type

2020 ◽  
Vol 65 (4) ◽  
pp. 503-519
Author(s):  
Arun Kumar Tripathy ◽  
Shyam Sundar Santra
Keyword(s):  
Nonlinear Equation ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Second Order ◽  
Similar Type ◽  
Necessary And Sufficient Conditions ◽  
Impulsive Systems ◽  
Necessary And Sufficient

In this work, the necessary and sufficient conditions for oscillation of a class of second order neutral impulsive systems are established and our impulse satisfies a discrete neutral nonlinear equation of similar type. Further, one illustrative example showing applicability of the new result is included.

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