Finite Difference Computational Method for Trajectory Controllability of a Delayed Damped System Governed by Fractional Differential Equation

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
P. Muthukumar ◽  
B. Ganesh Priya
Keyword(s):  
Finite Difference ◽  
Sufficient Conditions ◽  
Mathieu Equation ◽  
Computational Method ◽  
Scientific Models ◽  
Banach Fixed Point Theorem ◽  
Damped System ◽  
Fractional Differential ◽  
Necessary And Sufficient ◽  
System With Time Delay

In this paper, the trajectory controllability (T-controllability) of a nonlinear fractional-order damped system with time delay is studied. Existence and uniqueness of solution are obtained by using the Banach fixed point theorem and Green's function. Necessary and sufficient conditions of trajectory controllable for the nonlinear system are formulated and proved under a predefined trajectory. Modified fractional finite difference method is applied to the system for numerical approximation of its solution. The applicability of this technique is demonstrated by numerical simulation of two scientific models such as neuromechanical interaction in human snoring and fractional delayed damped Mathieu equation.

scholarly journals Constrained Controllability of theh-Difference Fractional Control Systems with Caputo Type Operator

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Ewa Pawluszewicz
Keyword(s):  
Sufficient Conditions ◽  
Fractional Operator ◽  
Discrete Time System ◽  
Time System ◽  
Fractional Systems ◽  
Constrained Controllability ◽  
Fractional Differential ◽  
Target Set ◽  
Fractional Control ◽  
Necessary And Sufficient

The problem of controllability to a given convex target set of linear fractional systems withh-difference fractional operator of Caputo type is studied. Necessary and sufficient conditions of controllability with constrained controllers for such systems are given. Problem of approximation of a continuous-time system with Caputo fractional differential by a discrete-time system withh-difference fractional operator of Caputo type is discussed.

On bounded nonoscillatory solutions of third-order nonlinear differential equations

2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Ivan Mojsej ◽  
Alena Tartaľová
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Banach Fixed Point Theorem ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Topological Approach ◽  
The Third ◽  
Necessary And Sufficient

AbstractThis paper is concerned with the asymptotic behavior of solutions of nonlinear differential equations of the third-order with quasiderivatives. We give the necessary and sufficient conditions guaranteeing the existence of bounded nonoscillatory solutions. Sufficient conditions are proved via a topological approach based on the Banach fixed point theorem.

Controllability of nonlinear stochastic fractional higher order dynamical systems

2019 ◽  
Vol 22 (4) ◽  
pp. 1063-1085
Author(s):  
R. Mabel Lizzy ◽  
K. Balachandran ◽  
Yong-Ki Ma
Keyword(s):  
Dynamical Systems ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Necessary And Sufficient Condition ◽  
Bounded Operators ◽  
Semilinear Systems ◽  
Operator Functions ◽  
Fractional System ◽  
Necessary And Sufficient ◽  
The Given

Abstract This paper deals with the study of controllability of stochastic fractional dynamical systems with 1 < α ≤ 2. Necessary and sufficient condition for controllability of linear stochastic fractional system is obtained. Sufficient conditions for controllability of stochastic fractional semilinear systems, integrodifferential systems, systems with neutral term, systems with delays in control and systems with Lévy noise is formulated and established. The solution is obtained in terms of Mittag-Leffler operator functions by considering bounded operators. The Banach fixed point theorem is used to obtain the desired results from an equivalent nonlinear integral equation of the given system.

Existence of mild solution of a class of nonlocal fractional order differential equation with not instantaneous impulses

2019 ◽  
Vol 22 (2) ◽  
pp. 495-508 ◽  
Author(s):  
Jayanta Borah ◽  
Swaroop Nandan Bora
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Mild Solution ◽  
Point Theorem ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Fractional Order Differential Equation ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential

Abstract In this article, we establish a set of sufficient conditions for the existence of mild solution of a class of fractional differential equations with not instantaneous impulses. The results are obtained by using Banach fixed point theorem and Krasnoselskii’s fixed point theorem. An example is presented for validation of result.

A NOVEL LESS DISSIPATION FINITE-DIFFERENCE LATTICE BOLTZMANN SCHEME FOR COMPRESSIBLE FLOWS

2012 ◽  
Vol 23 (11) ◽  
pp. 1250074 ◽  
Author(s):  
Q. CHEN ◽  
X. B. ZHANG
Keyword(s):  
Finite Difference ◽  
Lattice Boltzmann ◽  
Compressible Flows ◽  
Sufficient Conditions ◽  
Sufficient Conditions For Convergence ◽  
Necessary And Sufficient ◽  
Boltzmann Method ◽  
Lattice Boltzmann Scheme ◽  
Better Than ◽  
Good Agreement

In this paper, a new smoothness indicator is proposed to improve the finite-difference lattice Boltzmann method (FDLBM). The necessary and sufficient conditions for convergence are derived. A detailed analysis reveals that the convergence order is higher than that of the previous finite-difference scheme. The coupled double distribution function (DDF) model is used to describe discontinuity flows and verify the improvement. Numerical simulations of compressible flows with shock wave show that the improved finite-difference lattice Boltzmann scheme is accurate and has less dissipation. The numerical results are found to be in good agreement with the analytical results and better than those of the previous scheme.

Active Absorption of Viscously Damped System With Time Delay

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Yitshak M. Ram ◽  
Kumar Vikram Singh
Keyword(s):  
Time Delay ◽  
Passive Control ◽  
Degree Of Freedom ◽  
Sufficient Condition ◽  
Total Absorption ◽  
Necessary And Sufficient Condition ◽  
Controlled System ◽  
Damped System ◽  
Necessary And Sufficient ◽  
System With Time Delay

In general, it is not possible to obtain total motion absorption of a certain degree of freedom in a harmonically excited damped system by passive control. This paper presents a method of obtaining total absorption in viscously damped system by active control, including time delay, which is unavoidable in digital controlled system. The control is applied on one degree of freedom and the absorption is achieved at another point. This study is carried out by both complex and real analyses. The necessary and sufficient condition for obtaining total absorption is given. Examples demonstrate the various results.

scholarly journals Ulam Type Stability for a Coupled System of Boundary Value Problems of Nonlinear Fractional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Aziz Khan ◽  
Kamal Shah ◽  
Yongjin Li ◽  
Tahir Saeed Khan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Generalized Metric Space ◽  
Ulam Stability ◽  
Fractional Differential ◽  
Necessary And Sufficient

We discuss existence, uniqueness, and Hyers-Ulam stability of solutions for coupled nonlinear fractional order differential equations (FODEs) with boundary conditions. Using generalized metric space, we obtain some relaxed conditions for uniqueness of positive solutions for the mentioned problem by using Perov’s fixed point theorem. Moreover, necessary and sufficient conditions are obtained for existence of at least one solution by Leray-Schauder-type fixed point theorem. Further, we also develop some conditions for Hyers-Ulam stability. To demonstrate our main result, we provide a proper example.

scholarly journals Existence, Uniqueness, and Stability Solutions of Nonlinear System of Integral Equations

2020 ◽  
Vol 6 (2) ◽  
pp. 76-82
Author(s):  
Rizgar Issa Hasan
Keyword(s):  
Nonlinear System ◽  
Integral Equations ◽  
Sufficient Conditions ◽  
Successive Approximation Method ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Integral Equations ◽  
System Of Integral Equations ◽  
Compact Spaces ◽  
Necessary And Sufficient ◽  
Uniqueness Of A Solution

The aim of this work is to study the existence, uniqueness, and stability solutions of a new nonlinear system of integral equation by using Picard approximation (successive approximation) method and Banach fixed point theorem. The study of such nonlinear integral equations is more general and leads us to improve to extend the result of Butris. Theorems on the existence and uniqueness of a solution are established under some necessary and sufficient conditions on closed and bounded domains (compact spaces).

On the behavior of solutions of fractional differential equations on time scale via Hilfer fractional derivatives

2018 ◽  
Vol 21 (4) ◽  
pp. 1120-1138 ◽  
Author(s):  
Devaraj Vivek ◽  
Kuppusamy Kanagarajan ◽  
Seenith Sivasundaram
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of Solutions ◽  
Existence And Stability ◽  
Fractional Differential

Abstract In this paper, we study the existence and stability of Hilfer-type fractional differential equations (dynamic equations) on time scales. We obtain sufficient conditions for existence and uniqueness of solutions by using classical fixed point theorems such as Schauder's fixed point theorem and Banach fixed point theorem. In addition, Ulam stability of the proposed problem is also discussed. As in application, we provide an example to illustrate our main results.

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