297 research outputs found
Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives
The link between the treatments of constrained systems with fractional
derivatives by using both Hamiltonian and Lagrangian formulations is studied.
It is shown that both treatments for systems with linear velocities are
equivalent.Comment: 10 page
Fokker-Planck Equation with Fractional Coordinate Derivatives
Using the generalized Kolmogorov-Feller equation with long-range interaction,
we obtain kinetic equations with fractional derivatives with respect to
coordinates. The method of successive approximations with the averaging with
respect to fast variable is used. The main assumption is that the correlator of
probability densities of particles to make a step has a power-law dependence.
As a result, we obtain Fokker-Planck equation with fractional coordinate
derivative of order .Comment: LaTeX, 16 page
Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives
The classical fields with fractional derivatives are investigated by using
the fractional Lagrangian formulation.The fractional Euler-Lagrange equations
were obtained and two examples were studied.Comment: 9 page
Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics
We study fractional configurations in gravity theories and Lagrange
mechanics. The approach is based on Caputo fractional derivative which gives
zero for actions on constants. We elaborate fractional geometric models of
physical interactions and we formulate a method of nonholonomic deformations to
other types of fractional derivatives. The main result of this paper consists
in a proof that for corresponding classes of nonholonomic distributions a large
class of physical theories are modelled as nonholonomic manifolds with constant
matrix curvature. This allows us to encode the fractional dynamics of
interactions and constraints into the geometry of curve flows and solitonic
hierarchies.Comment: latex2e, 11pt, 27 pages, the variant accepted to CEJP; added and
up-dated reference
A Pseudospectral Algorithm for Solving Multipantograph Delay Systems on a Semi-Infinite Interval Using Legendre Rational Functions
A new Legendre rational pseudospectral scheme is proposed and developed for solving numerically systems of linear and nonlinear multipantograph equations on a semi-infinite interval. A Legendre rational collocation method based on Legendre rational-Gauss quadrature points is utilized to reduce the solution of such systems to systems of linear and nonlinear algebraic equations. In addition, accurate approximations are achieved by selecting few Legendre rational-Gauss collocation points. The numerical results obtained by this method have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively limited nodes used, the absolute error in our numerical solutions is sufficiently small
Time-Fractional KdV Equation: Formulation and Solution using Variational Methods
In this work, the semi-inverse method has been used to derive the Lagrangian
of the Korteweg-de Vries (KdV) equation. Then, the time operator of the
Lagrangian of the KdV equation has been transformed into fractional domain in
terms of the left-Riemann-Liouville fractional differential operator. The
variational of the functional of this Lagrangian leads neatly to Euler-Lagrange
equation. Via Agrawal's method, one can easily derive the time-fractional KdV
equation from this Euler-Lagrange equation. Remarkably, the time-fractional
term in the resulting KdV equation is obtained in Riesz fractional derivative
in a direct manner. As a second step, the derived time-fractional KdV equation
is solved using He's variational-iteration method. The calculations are carried
out using initial condition depends on the nonlinear and dispersion
coefficients of the KdV equation. We remark that more pronounced effects and
deeper insight into the formation and properties of the resulting solitary wave
by additionally considering the fractional order derivative beside the
nonlinearity and dispersion terms.Comment: The paper has been rewritten, 12 pages, 3 figure
The Fractionary Schr\"{o}dinger Equation, Green Functions and Ultradistributions
In this work, we generalize previous results about the Fractionary
Schr\"{o}dinger Equation within the formalism of the theory of Tempered
Ultradistributions. Several examples of the use of this theory are given. In
particular we evaluate the Green's function for a free particle in the general
case, for an arbitrary order of the derivative index.Comment: 32 pages. No figure
Hamilton-Jacobi formalism for Linearized Gravity
In this work we study the theory of linearized gravity via the
Hamilton-Jacobi formalism. We make a brief review of this theory and its
Lagrangian description, as well as a review of the Hamilton-Jacobi approach for
singular systems. Then we apply this formalism to analyze the constraint
structure of the linearized gravity in instant and front-form dynamics.Comment: To be published in Classical and Quantum Gravit
Characterization of a benzoic acid modified glassy carbon electrode expressed quantitatively by new statistical parameters
The main aim of this study is to characterize the nanosurface of the benzoic acid modified glassy carbon (GC) electrode by using a new statistical approach. In this study, the electrode surfaces were modified by cyclic voltametry in the potential range of +0.4 and -0.8 V at a scan rate 200 mV s-1 for four cycles versus Ag/Ag+ electrode in acetonitrile containing 0.1 M tetrabutylammonium tetraflouroborate (TBATFB). FT-IR spectra of the surface modifier molecules in both solid (GC and nanofilm (GC-benzoic acid)) forms were recorded in the spectral range 600-4000 cm-1. The FT-IR spectra of p-aminobenzoic acid were obtained by using KBr pellets. The above FT-IR spectra of both GC and its nanofilm with benzoic acid were processed by new statistical approach to reach optimal smoothing trend for the characterization of the modified electrode surface consisting of the nanofilm of GC-benzoic acid. In the frame of new statistical approach all measured spectra have been 'read' in terms of a set of universal statistical parameters. © 2008 Elsevier B.V. All rights reserved
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