Approximate Controllability of Semilinear Fractional Control Systems of Order $${{\alpha \in (1, 2]}}$$ α ∈ ( 1 , 2 ] with Infinite Delay

2015 ◽  
Vol 13 (5) ◽  
pp. 2539-2550 ◽  
Author(s):  
A. Shukla ◽  
N. Sukavanam ◽  
D. N. Pandey
Keyword(s):  
Control Systems ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Fractional Control

Approximate controllability of non-instantaneous impulsive semilinear measure driven control system with infinite delay via fundamental solution

2020 ◽  
Author(s):  
Surendra Kumar ◽  
Syed Mohammad Abdal
Keyword(s):  
Fundamental Solution ◽  
Differential Equations ◽  
Control Systems ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Existence Of A Solution ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
New Class

Abstract This article investigates a new class of non-instantaneous impulsive measure driven control systems with infinite delay. The considered system covers a large class of the hybrid system without any restriction on their Zeno behavior. The concept of measure differential equations is more general as compared to the ordinary impulsive differential equations; consequently, the discussed results are more general than the existing ones. In particular, using the fundamental solution, Krasnoselskii’s fixed-point theorem and the theory of Lebesgue–Stieltjes integral, a new set of sufficient conditions is constructed that ensures the existence of a solution and the approximate controllability of the considered system. Lastly, an example is constructed to demonstrate the effectiveness of obtained results.

scholarly journals Approximate Controllability of Fractional Integrodifferential Evolution Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
R. Ganesh ◽  
R. Sakthivel ◽  
N. I. Mahmudov ◽  
S. M. Anthoni
Keyword(s):  
Control System ◽  
Control Systems ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Semigroup Theory ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Approximately Controllable ◽  
Fractional Control ◽  
Lipschitz Conditions

This paper addresses the issue of approximate controllability for a class of control system which is represented by nonlinear fractional integrodifferential equations with nonlocal conditions. By using semigroup theory,p-mean continuity and fractional calculations, a set of sufficient conditions, are formulated and proved for the nonlinear fractional control systems. More precisely, the results are established under the assumption that the corresponding linear system is approximately controllable and functions satisfy non-Lipschitz conditions. The results generalize and improve some known results.

Approximate controllability of semilinear fractional differential systems of order 1 < q < 2 via resolvent operators

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5769-5781 ◽  
Author(s):  
Tingting Lian ◽  
Zhenbin Fan ◽  
Gang Li
Keyword(s):  
Control Systems ◽  
Approximate Controllability ◽  
Existence Results ◽  
Resolvent Operators ◽  
Differential Systems ◽  
Approximation Techniques ◽  
Fractional Differential Systems ◽  
Approximately Controllable ◽  
Fractional Differential ◽  
Fractional Control

Under a compactness assumption on the resolvent, some properties on relevant operators generated by resolvent are given. Existence results of fractional control systems are obtained by Schauder?s fixed point theorem and approximation techniques. Furthermore, the approximately controllable result is acquired under the assumption that the corresponding linear system is approximately controllable, which improves and extends some results on this topic.

Duality theory of fractional resolvents and applications to backward fractional control systems

2021 ◽  
Vol 24 (2) ◽  
pp. 541-558
Author(s):  
Shouguo Zhu ◽  
Gang Li
Keyword(s):  
Control System ◽  
Fractional Derivative ◽  
Control Systems ◽  
Diffusion Model ◽  
Duality Theory ◽  
Approximate Controllability ◽  
Fractional Diffusion ◽  
Variational Technique ◽  
Liouville Fractional Derivative ◽  
Fractional Control

Abstract We study the duality theory for fractional resolvents, extending and improving some corresponding theorems on semigroups. As applications, we develop the variational technique to analyze the finite-approximate controllability of a backward fractional control system with a right-sided Riemann-Liouville fractional derivative. Moreover, validity of our theoretical findings is given by a fractional diffusion model.

scholarly journals Controllability of Neutral Fractional Functional Equations with Impulses and Infinite Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
R. Ganesh ◽  
R. Sakthivel ◽  
Yong Ren ◽  
S. M. Anthoni ◽  
N. I. Mahmudov
Keyword(s):  
Control Systems ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Exact Controllability ◽  
Linear Control ◽  
Solution Operator ◽  
Controllability Problem ◽  
Fractional Control ◽  
Fixed Point Techniques ◽  
Fractional Functional

We examine the controllability problem for a class of neutral fractional integrodifferential equations with impulses and infinite delay. More precisely, a set of sufficient conditions are derived for the exact controllability of nonlinear neutral impulsive fractional functional equation with infinite delay. Further, as a corollary, approximate controllability result is discussed by assuming compactness conditions on solution operator. The results are established by using solution operator, fractional calculations, and fixed point techniques. In particular, the controllability of nonlinear fractional control systems is established under the assumption that the corresponding linear control system is controllable. Finally, an example is given to illustrate the obtained 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.

Sign in / Sign up

Export Citation Format

Share Document