相关论文: Twist of fractional oscillations

We derive the gravitational Lagrangian to all orders of curvature when the canonical constraint algebra is deformed by a phase space function as predicted by some studies into loop quantum cosmology. The deformation function seems to be…

We introduce a class of fractional Dirac type operators with time variable coefficients by means of a Witt basis, the Djrbashian-Caputo fractional derivative and the fractional Laplacian, both operators defined with respect to some given…

In this paper the Bagley-Torvik Equation is considered with the order of the damping term allowed to range between one and two. The solution is found to be representable as a convolution of trigonometric and exponential functions with the…

We investigate evolution equations for anomalous diffusion employing fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. Fractional diffusion equations…

Based on the requirement of covariance, we propose a new approach for generalizing fractional calculus in multi-dimensional space. As a first application we calculate an approximation for the ground state energy of the fractional…

For system of two ordinary differential equations of the second order representing autonomous non-conservative holonomic mechanical system, in case of dynamics such as one-frequency periodical oscillations, is found integrated invariant of…

In this paper we study a new generalization of the kinetic equation emerging in run-and-tumble models. We show that this generalization leads to a wide class of generalized fractional kinetic (GFK) and telegraph-type equations depending by…

Fractional supersymmetric quantum mechanics of order $\lambda$ is realized in terms of the generators of a generalized deformed oscillator algebra and a Z$_{\lambda}$-grading structure is imposed on the Fock space of the latter. This…

The goal of our work is to investigate the oscillation and asymptotic properties of a class of difference equations with a condition. In contrast to most previous studies, the oscillation of the investigated equation is obtained with only…

Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…

A macroscopic characterization of fractals showing up a structural transition from dense to multibranched growth is made using optical diffraction theory. Such fractals are generated via the numerical solution of the 2D Poisson and…

A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables…

We consider a partially hinged rectangular plate and its normal modes. There are two families of modes, longitudinal and torsional. We study the variation of the corresponding eigenvalues under domain deformations. We investigate the…

A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector…

We speculate on the role of relativistic versions of delayed differential equations in fundamental physics. Relativistic invariance implies that we must consider both advanced and retarded terms in the equations, so we refer to them as…

We generalize the generalized-squeezing problem to include fractional values of the squeezing order $n$. This approach allows us to determine the locations of critical points at which qualitative changes in behaviour occur and accurately…

Fractional analysis is applied to describe classical dynamical systems. Fractional derivative can be defined as a fractional power of derivative. The infinitesimal generators {H, .} and L=G(q,p) \partial_q+F(q,p) \partial_p, which are used…

The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…

In this work we study the solutions to some fractional higher-order equations. Special cases in which time-fractional derivatives take integer values are also examined and the explicit solutions are presented. Such solutions can be…

A novel approach is introduced for obtaining precise solutions of the pairing Hamiltonian for tetraquarks, which utilizes an algebraic technique in infinite dimensions. The parameters involved in the transition phase are calibrated based on…