相关论文: Fractional Generalization of Liouville Equations

In this paper we propose a lattice analog of phase-space fractional Liouville equation. The Liouville equation for phase-space lattice with long-range jumps of power-law types is suggested. We prove that the continuum limit transforms this…

We consider a nonlinear parabolic equation of fractional order in space and propose its numerical discretization. The fractional derivative is defined through a functional analytic setting, rather than the traditional definition of…

In this work we present a new approach on studying dynamical systems. Combining the two ways of expressing the uncertainty, using probabilistic theory and credibility theory, we have research the generalized fractional hybrid equations. We…

Motivated by the classification of solutions of harmonic functions, we investigate Liouville type theorems for the fractional Navier-Stokes equations in $\mathbb{R}^3$ under some conditions on the boundedness of fractional derivatives. We…

This paper is in continuation of the authors' recently published paper (Journal of Mathematical Physics 55(2014)083519) in which computational solutions of an unified reaction-diffusion equation of distributed order associated with Caputo…

We explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant stochastic generalization of Hamiltonian dynamics. The motivation for this project, started with this paper, is to assign…

The goal of this communication is to propose a generalized notion of the "traditional derivative". This generalization includes the fractional derivatives such as the Riemann-Liouville, Gruenwald-Letnikov, Weyl, Riesz, Caputo, Marchaud…

The objective of this paper is to derive analytical solutions of fractional order Laplace, Poisson and Helmholtz equations in two variables derived from the corresponding standard equations in two dimensions by replacing the integer order…

A fractional generalization of variations is used to define a stability of non-integer order. Fractional variational derivatives are suggested to describe the properties of dynamical systems at fractional perturbations. We formulate…

A one dimensional fractional diffusion model with the Riemann-Liouville fractional derivative is studied. First, a second order discretization for this derivative is presented and then an unconditionally stable weighted average finite…

We suggest an extension of the Hilbert Phase Space formalism, which appears to be naturally suited for application to the dissipative (open) quantum systems, such as those described by the non-stationary (time-dependent) Hamiltonians…

In this paper, a fractional generalization of the wave equation that describes propagation of damped waves is considered. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional derivatives of…

This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the…

A large class of classical dynamical systems with an external rapidly oscillating driving action is considered and the effective Hamiltonian-like equations for the mean motion are obtained. The respective Liouville equation for the…

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…

We derive the fractional generalization of the Ginzburg-Landau equation from the variational Euler-Lagrange equation for fractal media. To describe fractal media we use the fractional integrals considered as approximations of integrals on…

Generalization of the Kac integral and Kac method for paths measure based on the Levy distribution has been used to derive fractional diffusion equation. Application to nonlinear fractional Ginzburg-Landau equation is discussed.

In this PhD thesis we introduce a generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives, and study them using standard (indirect) and direct methods. In…

A possibility to represent the standard model of fundamental particles covariant derivatives by means of approximate generalized fractional Riemann-Liouville derivatives of multifractal time and space model is shown.

In this paper, we investigate the solutions for a generalized fractional diffusion equation that extends some known diffusion equations by taking a spatial time-dependent diffusion coefficient and an external force into account, which…