Related papers: Fractional Canonical Quantization: a Parallel with…

The similarity between classical and quantum physics is large enough to make an investigation of quantization methods a worthwhile endeavour. As history has shown, Dirac's canonical quantization method works reasonably well in the case of…

In this paper, we first deal with the general fractional derivatives of arbitrary order defined in the Riemann-Liouville sense. In particular, we deduce an explicit form of their null space and prove the second fundamental theorem of…

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…

In [1], an operator was introduced which acts parallel to the Riemann-Liouville differintegral on a transformation of the space of real analytic functions and commutes with itself. This paper aims to extend the technique - and its defining…

Wentzel, Kramers, Brillouin (WKB) approximation for fractional systems is investigated in this paper using the fractional calculus. In the fractional case the wave function is constructed such that the phase factor is the same as the…

We start with a general governing equation for diffusion transport, written in a conserved form, in which the phenomenological flux laws can be constructed in a number of alternative ways. We pay particular attention to flux laws that can…

We investigate fractional Brownian motion with a microscopic random-matrix model and introduce a fractional Langevin equation. We use the latter to study both sub- and superdiffusion of a free particle coupled to a fractal heat bath. We…

Fractional calculus represents a natural tool for describing relativistic phenomena in pseudo-Euclidean space-time. In this study, Fractional modified special relativity is presented. We obtain fractional generalized relation for the time…

With the discovery of new superconductors there was a running to find the justifications for the new properties found in these materials. In order to describe these new effects some theories were adapted and some others have been tried. In…

Using arbitrary symplectic structures and parametrization invariant actions, we develop a formalism, based on Dirac's quantization procedure, that allows us to consider theories with both space-space as well as space-time noncommutativity.…

It is shown that the Weyl fractional derivative can quantize an open system. A fractional kicked rotor is studied in the framework of the fractional Schrodinger equation. The system is described by the non-Hermitian Hamiltonian by virtue of…

We study operators that are generalizations of the classical Riemann-Liouville fractional integral, and of the Riemann-Liouville and Caputo fractional derivatives. A useful formula relating the generalized fractional derivatives is proved,…

The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for…

We extend the Worldline Monte Carlo approach to computationally simulating the Feynman path integral of non-relativistic multi-particle quantum-mechanical systems. We show how to generate an arbitrary number of worldlines distributed…

Solution of fractional differential equations is an emerging area of present day research because such equations arise in various applied fields. In this paper we have developed analytical method to solve the system of fractional…

We investigate the space time fractional nonlinear Schrodinger equation (FNLSE) incorporating the modified Riemann Liouville derivative introduced by Jumari. The equation is characterized by two parameters: the fractional derivative…

Noncommutative differential calculus on quantum Minkowski space is not separated with respect to the standard generators, in the sense that partial derivatives of functions of a single generator can depend on all other generators. It is…

We discuss the relationships between some classical representations of the fractional Brownian motion, as a stochastic integral with respect to a standard Brownian motion, or as a series of functions with independent Gaussian coefficients.…

In this paper, we propose a new model of fractional mimetic dark matter based on the fractional action-like variational approach FALVA implementation of fractionality. The model is non-local at classical level and its equations of motion…

We propose a framework for fitting fractional polynomials models as special cases of Bayesian Generalized Nonlinear Models, applying an adapted version of the Genetically Modified Mode Jumping Markov Chain Monte Carlo algorithm. The…