scholarly journals Existence and approximate controllability of non-autonomous functional impulsive evolution inclusions in Banach spaces

2022 ◽  
Vol 307 ◽  
pp. 83-113
Author(s):  
S. Arora ◽  
Manil T. Mohan ◽  
J. Dabas
Keyword(s):  
Banach Spaces ◽  
Approximate Controllability ◽  
Evolution Inclusions

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.

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

scholarly journals Evolution Inclusions in Banach Spaces under Dissipative Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 750
Author(s):  
Tzanko Donchev ◽  
Shamas Bilal ◽  
Ovidiu Cârjă ◽  
Nasir Javaid ◽  
Alina I. Lazu
Keyword(s):  
Banach Spaces ◽  
Differential Inclusions ◽  
Qualitative Properties ◽  
Evolution Inclusions ◽  
Fully Nonlinear ◽  
Limit Solution ◽  
Nonlinear Differential Inclusions ◽  
Limit Solutions ◽  
Lipschitz Conditions ◽  
Integral Solutions

We develop a new concept of a solution, called the limit solution, to fully nonlinear differential inclusions in Banach spaces. That enables us to study such kind of inclusions under relatively weak conditions. Namely we prove the existence of this type of solutions and some qualitative properties, replacing the commonly used compact or Lipschitz conditions by a dissipative one, i.e., one-sided Perron condition. Under some natural assumptions we prove that the set of limit solutions is the closure of the set of integral solutions.

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