On Constrained Systems Within Caputo Derivatives

2007 ◽  
Author(s):  
Dumitru Baleanu
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Variational Principles ◽  
Constrained Systems ◽  
Control Problems ◽  
Fractional Dynamics ◽  
Caputo Derivatives ◽  
Fractional Dynamical System

The constraints systems play a very important role in physics and engineering. The fractional variational principles were successfully applied to control problems as well as to construct the phase space of a fractional dynamical system. In this paper the fractional dynamics of discrete constrained systems is presented and the notion of the reduced phase-space is analyzed. One system possessing two primary first class constraints is analyzed in detail.

Fractional Constrained Systems and Caputo Derivatives

2008 ◽  
Vol 3 (2) ◽  
Author(s):  
Dumitru Baleanu
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Variational Principles ◽  
Constrained Systems ◽  
Control Problems ◽  
Fractional Dynamics ◽  
Constrained System ◽  
Caputo Derivatives ◽  
Fractional Dynamical System ◽  
Made In

During the last few years, remarkable developments have been made in the theory of the fractional variational principles and their applications to control problems and fractional quantization issue. The variational principles have been used in physics to construct the phase space of a fractional dynamical system. Based on the Caputo derivatives, the fractional dynamics of discrete constrained systems is presented and the notion of the reduced phase space is discussed. Two examples of discrete constrained system are analyzed in detail.

Fractional Mechanics on the Extended Phase Space

2009 ◽  
Author(s):  
Dumitru Baleanu ◽  
Sami I. Muslih ◽  
Alireza K. Golmankhaneh ◽  
Ali K. Golmankhaneh ◽  
Eqab M. Rabei
Keyword(s):  
Phase Space ◽  
Variational Principles ◽  
Fractional Dynamics ◽  
Classical Dynamics ◽  
Extended Phase Space ◽  
Science And Engineering ◽  
Extended Phase ◽  
Potential Applications ◽  
Fractional Mechanics ◽  
Complex Phenomena

Fractional calculus has gained a lot of importance and potential applications in several areas of science and engineering. The fractional dynamics and the fractional variational principles started to be used intensively as an alternative tool in order to describe the physical complex phenomena. In this paper we have discussed the fractional extension of the classical dynamics. The fractional Hamiltonian is constructed and the fractional generalized Poisson’s brackets on the extended phase space is established.

PATH INTEGRAL QUANTIZATION OF SUPERSTRING

2010 ◽  
Vol 25 (02) ◽  
pp. 135-141
Author(s):  
H. A. ELEGLA ◽  
N. I. FARAHAT
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Path Integral ◽  
Equations Of Motion ◽  
Singular System ◽  
Constrained Systems ◽  
Classical Structure ◽  
Path Integral Quantization ◽  
Total Differential

Motivated by the Hamilton–Jacobi approach of constrained systems, we analyze the classical structure of a four-dimensional superstring. The equations of motion for a singular system are obtained as total differential equations in many variables. The path integral quantization based on Hamilton–Jacobi approach is applied to quantize the system, and the integration is taken over the canonical phase space coordinates.

Fractal–fractional dynamical system of Typhoid disease including protection from infection

2021 ◽  
Author(s):  
Qu Haidong ◽  
Mati ur Rahman ◽  
Muhammad Arfan ◽  
Mehdi Salimi ◽  
Soheil Salahshour ◽  
...  
Keyword(s):  
Dynamical System ◽  
Fractional Dynamical System

scholarly journals A Dynamical System with q-Deformed Phase Space Represented in Ordinary Variable Spaces

2010 ◽  
Vol 124 (6) ◽  
pp. 1019-1035
Author(s):  
S. Naka ◽  
H. Toyoda ◽  
T. Takanashi
Keyword(s):  
Dynamical System ◽  
Phase Space

scholarly journals A VARIATIONAL FORMULATION OF SYMPLECTIC NONCOMMUTATIVE MECHANICS

2007 ◽  
Vol 04 (05) ◽  
pp. 789-805 ◽  
Author(s):  
IGNACIO CORTESE ◽  
J. ANTONIO GARCÍA
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Variational Principle ◽  
Configuration Space ◽  
Variational Formulation ◽  
Noncommutative Space ◽  
First Order ◽  
Dynamical Properties ◽  
Definition Of ◽  
Space Noncommutativity

The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to understand the inherent space noncommutativity, we propose a variational principle for noncommutative dynamical systems in configuration space, based on results of our previous work [18]. We hope that this variational formulation in configuration space can be of help to elucidate the definition of some global and dynamical properties of classical and quantum noncommutative space.

Phase space geometry of constrained systems

1995 ◽  
Vol 105 (3) ◽  
pp. 1539-1545 ◽  
Author(s):  
V. P. Pavlov ◽  
A. O. Starinetz
Keyword(s):  
Phase Space ◽  
Constrained Systems ◽  
Space Geometry ◽  
Phase Space Geometry

On Fractional Hamilton Formulation Within Caputo Derivatives

2007 ◽  
Author(s):  
Dumitru Baleanu ◽  
Sami I. Muslih ◽  
Eqab M. Rabei
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivatives ◽  
Variational Principles ◽  
Hamiltonian Dynamics ◽  
Fractional Integration ◽  
Fractional Dynamics ◽  
Classical Dynamics ◽  
Lagrange Equations ◽  
Caputo Fractional Derivatives ◽  
Non Locality

The fractional Lagrangian and Hamiltonian dynamics is an important issue in fractional calculus area. The classical dynamics can be reformulated in terms of fractional derivatives. The fractional variational principles produce fractional Euler-Lagrange equations and fractional Hamiltonian equations. The fractional dynamics strongly depends of the fractional integration by parts as well as the non-locality of the fractional derivatives. In this paper we present the fractional Hamilton formulation based on Caputo fractional derivatives. One example is treated in details to show the characteristics of the fractional dynamics.

scholarly journals ON BARYON NUMBER NONCONSERVATION IN TWO-DIMENSIONAL O(2N+1) QCD

2010 ◽  
Vol 25 (06) ◽  
pp. 1253-1266
Author(s):  
TAMAR FRIEDMANN
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Matrix Models ◽  
Gauge Group ◽  
Baryon Number ◽  
Two Dimensional ◽  
Infinite Dimensional ◽  
Field Approach ◽  
Large N ◽  
Classical Dynamical System

We construct a classical dynamical system whose phase space is a certain infinite-dimensional Grassmannian manifold, and propose that it is equivalent to the large N limit of two-dimensional QCD with an O (2N+1) gauge group. In this theory, we find that baryon number is a topological quantity that is conserved only modulo 2. We also relate this theory to the master field approach to matrix models.

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