Approximate Controllability for a Class of Second-Order Stochastic Evolution Inclusions of Clarke’s Subdifferential Type

2018 ◽  
Vol 73 (1) ◽  
Author(s):  
V. Vijayakumar
Keyword(s):  
Approximate Controllability ◽  
Second Order ◽  
Stochastic Evolution ◽  
Evolution Inclusions ◽  
Clarke’S Subdifferential

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 Results on the approximate controllability of fractional hemivariational inequalities of order $1< r<2$

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. Mohan Raja ◽  
V. Vijayakumar ◽  
Le Nhat Huynh ◽  
R. Udhayakumar ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Fixed Point ◽  
Control Systems ◽  
Approximate Controllability ◽  
Hemivariational Inequalities ◽  
Evolution Inclusions ◽  
Fractional Systems ◽  
Cosine Families ◽  
Fixed Point Approach ◽  
Semilinear Control Systems ◽  
Theoretical Results

AbstractIn this paper, we investigate the approximate controllability of fractional evolution inclusions with hemivariational inequalities of order $1< r<2$ 1 < r < 2 . The main results of this paper are verified by using the fractional theories, multivalued analysis, cosine families, and fixed-point approach. At first, we discuss the existence of the mild solution for the class of fractional systems. After that, we establish the approximate controllability of linear and semilinear control systems. Finally, an application is presented to illustrate our theoretical results.

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