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 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.

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 Analytical Study of Two Nonlinear Coupled Hybrid Systems Involving Generalized Hilfer Fractional Operators

2021 ◽  
Vol 5 (4) ◽  
pp. 178
Author(s):  
Mohammed A. Almalahi ◽  
Omar Bazighifan ◽  
Satish K. Panchal ◽  
S. S. Askar ◽  
Georgia Irina Oros
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fractional Derivatives ◽  
Analytical Study ◽  
Sufficient Conditions ◽  
Coupled Systems ◽  
Krasnoselskii Fixed Point Theorem ◽  
Hybrid Fixed Point Theorem ◽  
Fractional Differential

In this research paper, we dedicate our interest to an investigation of the sufficient conditions for the existence of solutions of two new types of a coupled systems of hybrid fractional differential equations involving ϕ-Hilfer fractional derivatives. The existence results are established in the weighted space of functions using Dhage’s hybrid fixed point theorem for three operators in a Banach algebra and Dhage’s helpful generalization of Krasnoselskii fixed- point theorem. Finally, simulated examples are provided to demonstrate the obtained results.

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.

On a fixed point theorem and its stochastic equivalent

1975 ◽  
Vol 12 (03) ◽  
pp. 605-611 ◽  
Author(s):  
Joseph A. Yahav
Keyword(s):  
Fixed Point ◽  
Markov Process ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Limiting Distribution

A discrete-time Markov process on the interval [0, 1] is considered. Sufficient conditions for the existence of a unique stationary limiting distribution are given.

scholarly journals The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations with Infinite Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Azizollah Babakhani ◽  
Dumitru Baleanu ◽  
Ravi P. Agarwal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Infinite Delay ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

We prove the existence and uniqueness of solutions for two classes of infinite delay nonlinear fractional order differential equations involving Riemann-Liouville fractional derivatives. The analysis is based on the alternative of the Leray-Schauder fixed-point theorem, the Banach fixed-point theorem, and the Arzela-Ascoli theorem inΩ={y:(−∞,b]→ℝ:y|(−∞,0]∈ℬ}such thaty|[0,b]is continuous andℬis a phase space.

scholarly journals Multiple Positive Symmetric Solutions top-Laplacian Dynamic Equations on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-27
Author(s):  
You-Hui Su ◽  
Can-Yun Huang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Discrete Equations ◽  
Special Cases ◽  
Krasnosel’Skii’S Fixed Point Theorem

This paper makes a study on the existence of positive solution top-Laplacian dynamic equations on time scales𝕋. Some new sufficient conditions are obtained for the existence of at least single or twin positive solutions by using Krasnosel'skii's fixed point theorem and new sufficient conditions are also obtained for the existence of at least triple or arbitrary odd number positive solutions by using generalized Avery-Henderson fixed point theorem and Avery-Peterson fixed point theorem. As applications, two examples are given to illustrate the main results and their differences. These results are even new for the special cases of continuous and discrete equations, as well as in the general time-scale setting.

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