scholarly journals On the controllability of fractional dynamical systems

2012 ◽  
Vol 22 (3) ◽  
pp. 523-531 ◽  
Author(s):  
Krishnan Balachandran ◽  
Jayakumar Kokila
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Matrix Function ◽  
Sufficient Conditions ◽  
Schauder’S Fixed Point Theorem ◽  
Finite Dimensional ◽  
Linear And Nonlinear ◽  
Controllability Grammian

Abstract This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder’s fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.

scholarly journals Global relative controllability of fractional stochastic dynamical systems with distributed delays in control

2014 ◽  
Vol 32 (2) ◽  
pp. 55 ◽  
Author(s):  
Toufik Guendouzi ◽  
Iqbal Hamada
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Banach Fixed Point Theorem ◽  
Stochastic Dynamical Systems ◽  
Relative Controllability ◽  
Finite Dimensional ◽  
Linear And Nonlinear ◽  
Controllability Grammian

This paper is concerned with the global relative controllability of linear and nonlinear fractional stochastic dynamical systems with distributed delays in control for finite dimensional spaces. Sufficient conditions for controllability results are obtained using the Banach fixed point theorem and the controllability Grammian matrix which is dened by the Mittag-Leffler matrix function. An example is provided to illustrate the theory.

New sufficient conditions for contractively widely more generalized hybrid mappings to have a fixed point

2016 ◽  
Vol 09 (04) ◽  
pp. 1650082
Author(s):  
Toshiharu Kawasaki
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
The Other ◽  
Nonlinear Anal ◽  
Linear And Nonlinear

Hasegawa, Kawasaki and Kobayashi [Fixed point theorems for contractively widely more generalized hybrid mappings in metric spaces, to appear in Linear and Nonlinear Anal.] introduced the concept of contractively widely more generalized hybrid mappings in a metric space. On the other hand, Bogin [A generalization of a fixed point theorem of Goebel, Kirk and Shimi, Canad. Math. Bull. 19 (1976) 7–12] showed a fixed point theorem. However, Bogin’s result is not included in our results. In this paper, we consider new sufficient conditions as to cover the Bogin’s fixed point theorem for contractively widely more generalized hybrid mappings to have a fixed point.

scholarly journals The controllability of nonlinear implicit fractional delay dynamical systems

2017 ◽  
Vol 27 (3) ◽  
pp. 501-513 ◽  
Author(s):  
Rajagopal Joice Nirmala ◽  
Krishnan Balachandran
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fractional Derivatives ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Multiple Delays ◽  
Darbo Fixed Point Theorem ◽  
Fractional Delay

AbstractThis paper is concerned with the controllability of nonlinear fractional delay dynamical systems with implicit fractional derivatives for multiple delays and distributed delays in control variables. Sufficient conditions are obtained by using the Darbo fixed point theorem. Further, examples are given to illustrate the theory.

scholarly journals Schauder’s fixed-point theorem in approximate controllability problems

2016 ◽  
Vol 26 (2) ◽  
pp. 263-275 ◽  
Author(s):  
Artur Babiarz ◽  
Jerzy Klamka ◽  
Michał Niezabitowski
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Dynamic Systems ◽  
Approximate Controllability ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Schauder’S Fixed Point Theorem ◽  
Differential Systems ◽  
Schauder's Fixed Point Theorem

AbstractThe main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems in infinite-dimensional spaces. The presented investigation focuses on obtaining sufficient conditions for approximate controllability of various types of dynamic systems using Schauder’s fixed-point theorem. We describe the results of approximate controllability for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions, impulsive neutral functional evolution integro-differential systems, stochastic impulsive systems with control-dependent coefficients, nonlinear impulsive differential systems, and evolution systems with nonlocal conditions and semilinear evolution equation.

Controllability of nonlinear perturbations of linear systems with distributed delays in control

Robotica ◽  
1985 ◽  
Vol 3 (2) ◽  
pp. 89-91 ◽  
Author(s):  
K. Balachandran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Linear Systems ◽  
Point Theorem ◽  
Control Variable ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Schauder’S Fixed Point Theorem ◽  
Nonlinear Perturbations ◽  
Relative Controllability

SUMMARYSufficient conditions are derived for the relative controllability of nonlinear perturbations of linear systems with distributed delays in control variable. The results are a generalization of previous results and are obtained by using Schauder's fixed point theorem.

scholarly journals Relative controllability of nonlinear neutral Volterra integrodifferential systems

1996 ◽  
Vol 37 (3) ◽  
pp. 346-353 ◽  
Author(s):  
K. Balachandran ◽  
J. P. Dauer
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Schauder’S Fixed Point Theorem ◽  
Control Variables ◽  
Relative Controllability ◽  
Schauder's Fixed Point Theorem

AbstractSufficient conditions are derived for the relative controllability of nonlinear neutral Volterra integrodifferential systems with distributed delays in the control variables. The results are a generalization of previous results and are obtained by using Schauder's fixed-point theorem.

scholarly journals Existence of Positive Periodic Solutions for a Class ofn-Species Competition Systems with Impulses

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Peilian Guo ◽  
Yansheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Species Competition ◽  
Positive Periodic Solutions ◽  
The Fixed Point Theorem

By using the fixed point theorem on cone, some sufficient conditions are obtained on the existence of positive periodic solutions for a class ofn-species competition systems with impulses. Meanwhile, we point out that the conclusion of (Yan, 2009) is incorrect.

scholarly journals Uniqueness and Stability Results on Non-local Stochastic Random Impulsive Integro-Differential Equations

2021 ◽  
Vol 2 (3) ◽  
pp. 9-20
Author(s):  
VARSHINI S ◽  
BANUPRIYA K ◽  
RAMKUMAR K ◽  
RAVIKUMAR K
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Local Conditions ◽  
Non Local ◽  
Inequality Techniques ◽  
Stability Results

The paper is concerned with stochastic random impulsive integro-differential equations with non-local conditions. The sufficient conditions guarantees uniqueness of mild solution derived using Banach fixed point theorem. Stability of the solution is derived by incorporating Banach fixed point theorem with certain inequality techniques.

scholarly journals PERIODIC SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH SIGN-CHANGING POTENTIAL

2010 ◽  
Vol 82 (3) ◽  
pp. 437-445 ◽  
Author(s):  
JIFENG CHU ◽  
ZIHENG ZHANG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Second Order ◽  
Schauder’S Fixed Point Theorem ◽  
Positive Periodic Solutions ◽  
Singular Differential Equations ◽  
Attractive Case

AbstractIn this paper we study the existence of positive periodic solutions to second-order singular differential equations with the sign-changing potential. Both the repulsive case and the attractive case are studied. The proof is based on Schauder’s fixed point theorem. Recent results in the literature are generalized and significantly improved.

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