Related papers: Fractional Particle with Fractional First Derivati…
Fractional electromagnetic field theory describes electromagnetic wave propagation through the complex, nonlocal, dissipative, fractal and also recent artificially engineered materials know as fractional metamaterials. In this theory using…
The paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and…
In this paper the author presents the results of the preliminary investigation of fractional dynamical systems based on the results of numerical simulations of fractional maps. Fractional maps are equivalent to fractional differential…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
The fractional quantum and statistical mechanics have been developed via new path integrals approach.
We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model…
In this article, we propose new proportional fractional operators generated from local proportional derivatives of a function with respect to another function. We present some properties of these fractional operators which can be also…
Critical analyses of well-known methods of derivation of kinetic and hydrodynamic equations is presented. Another method of derivation of kinetic and hydrodynamic equations from classic mechanics is described. It is shown that equations of…
We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors…
In this article, we introduce a new general definition of fractional derivative and fractional integral, which depends on an unknown kernel. By using these definitions, we obtain the basic properties of fractional integral and fractional…
Fractional calculus is a couple of centuries old, but its development has been less embraced and it was only within the last century that a program of applications for physics started. Regarding quantum physics, it has been only in the…
Using the fractional integration and differentiation on R we build the fractional jet fibre bundle on a differentiable manifold and we emphasize some important geometrical objects. Euler-Lagrange fractional equations are described. Some…
We present the technique of derivation of a theory to obtain an $(n+1)f$-degrees-of-freedom theory from an $f$-degrees-of-freedom theory and show that one can calculate all of the quantities of the derived theory from those of the original…
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and…
A model for the dynamics of a classical point charged particle interacting with higher order jet fields is introduced. In this model, the dynamics of the charged particle is described by an implicit ordinary second order differential…
We generalize the differential representation of the operators of the Galilean algebras to include fractional derivatives. As a result a whole new class of scale invariant Galilean algebras are obtained. The first member of this class has…
Using the molecular dynamics method, we examine a discrete deterministic model for the motion of spherical particles in three-dimensional space. The model takes into account multiparticle collisions in arbitrary forms. Using fractional…
Power laws in time and frequency appear in fields such as linear viscoelasticity and acoustics, viscous boundary layer problems, and dielectrics. This is consistent with fractional derivatives in the fundamental descriptions, since power…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
This paper suggests a new way to compute the path integral for simple quantum mechanical systems. The new algorithm originated from previous research in string theory. However, its essential simplicity is best illustrated in the case of a…