Related papers: Covariance in Fractional Calculus
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…
We introduce a quantum information method for measuring fractional charges in ballistic quantum wires generalizing bipartite fluctuations to the chiral quasiparticles in Luttinger liquids, i.e. analyzing and summing charge and current…
This work further develops the properties of fractional differential forms. In particular, finite dimensional subspaces of fractional form spaces are considered. An inner product, Hodge dual, and covariant derivative are defined. Coordinate…
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic…
If we cannot obtain all terms of a series, or if we cannot sum up a series, we have to turn to the partial sum approximation which approximate a function by the first several terms of the series. However, the partial sum approximation often…
We calculate the partition function of a harmonic oscillator with quasi-periodic boundary conditions using the zeta-function method. This work generalizes a previous one by Gibbons and contains the usual bosonic and fermionic oscillators as…
The theory of fractional calculus is attracting a lot of attention from mathematicians as well as physicists. The fractional generalisation of the well-known ordinary calculus is being used extensively in many fields, particularly in…
Fractional systems with Riemann-Liouville derivatives are considered. The initial memory value problem is posed and studied. We obtain explicit steering laws with respect to the values of the fractional integrals of the state variables. The…
In this paper fractional generalization of Liouville equation is considered. We derive fractional analog of normalization condition for distribution function. Fractional generalization of the Liouvile equation for dissipative and…
In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…
We consider the fractional oscillator being a generalization of the conventional linear oscillator in the framework of fractional calculus. It is interpreted as an ensemble average of ordinary harmonic oscillators governed by stochastic…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered ``anomalous''. It is often used when traditional integer derivatives models fail to represent cases…
In the preceding Part II, we derived variational equations for the phonon Fourier amplitudes and for the Fourier amplitudes of the fractional contribution of the electronic bands to the trial variational state. These equations are now…
We present a systematic study of the Rayleigh--Ritz variational method for quantum oscillators in the Segal--Bargmann space. We rigorously derive the normalizability condition $|\alpha| < \tfrac{1}{2}$ for generalized Gaussian trial…
We use a particular fractional generalization of the ordinary differential equations that we apply to the Riccati equation of constant coefficients. By this means the latter is transformed into a modified Riccati equation with the free term…
The aim of this paper is to bring together two approaches to non-conservative systems -- the generalized variational principle of Herglotz and the fractional calculus of variations. Namely, we consider functionals whose extrema are sought,…
The reduced basis method is used to construct a "universal" basis of Dirac orbitals that may be applicable throughout the nuclear chart to calibrate covariant energy density functionals. Relative to our earlier work using the…
Fractional variational approach has gained much attention in recent years. There are famous fractional derivatives such as Caputo derivative, Riesz derivative and Riemann-Liouville derivative. Several versions of fractional variational…
A new scheme of field quantization is proposed. Instead of associating with different frequencies different oscillators we begin with a single oscillator that can exist in a superposition of different frequencies. The idea is applied to the…