Approximate Controllability Results for Impulsive Partial Functional Nonlocal Integro-differential Evolution Systems through Resolvent Operators

2018 ◽  
Vol 7 (3) ◽  
pp. 305-325
Author(s):  
Mahalingam Nagaraj ◽  
Selvaraj Suganya ◽  
Dumitru Baleanu ◽  
Mani Mallika Arjunan
Keyword(s):  
Differential Evolution ◽  
Approximate Controllability ◽  
Resolvent Operators ◽  
Evolution Systems

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 the finite approximate controllability for Hilfer fractional evolution systems with nonlocal conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 529-539
Author(s):  
Xianghu Liu
Keyword(s):  
Approximate Controllability ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Evolution System ◽  
Controlled Systems ◽  
Uniqueness Of The Solution ◽  
Fractional Evolution Systems ◽  
Evolution Systems

Abstract The aim of this study is to investigate the finite approximate controllability of certain Hilfer fractional evolution systems with nonlocal conditions. To achieve this, we first transform the mild solution of the Hilfer fractional evolution system into a fixed point problem for a condensing map. Then, by using the topological degree approach, we present sufficient conditions for the existence and uniqueness of the solution of the Hilfer fractional evolution systems. Using the variational approach, we obtain sufficient conditions for the finite approximate controllability of semilinear controlled systems. Finally, an example is provided to illustrate main results.

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.

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