Related papers: Covariance in Fractional Calculus
In this paper we utilize the covariance of Ricatti equation with respect to linear fractional transformations to define classes of conformally equivalent second order differential equations. This motivates then the introduction of…
Using the method of the Laplace transform, we consider fractional oscillations. They are obtained by the time-clock randomization of ordinary harmonic vibrations. In contrast to sine and cosine, the functions describing the fractional…
We formulate fractional difference equations of Riemann-Liouville and Caputo type in a functional analytical framework. Main results are existence of solutions on Hilbert space-valued weighted sequence spaces and a condition for stability…
In a previous work, we reported exact results of energies of the ground state in the fractional quantum Hall effect (FQHE) regime for systems with up to $N_{\text{e}} = 6$ electrons at the filling factor $\nu = 1/3$ by using the method of…
We start by presenting a brief summary of fractional quantum mechanics, as means to convey a motivation towards fractional quantum cosmology. Subsequently, such application is made concrete with the assistance of a case study. Specifically,…
We develop a simple and accurate method to solve fractional variational and fractional optimal control problems with dependence on Caputo and Riemann-Liouville operators. Using known formulas for computing fractional derivatives of…
Variation principle has been developed to calculate many-particle effects in crystals. Within the framework of quasi-particle concept the variation principle has been used to find one-electron states with taking into account of effects due…
We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.
Fermion-number fractionalization without breaking of time-reversal symmetry was recently demonstrated for a field theory in $(2+1)$-dimensional space and time that describes the couplings between massive Dirac fermions, a complex-valued…
In this note we prove some new results about the application of Wright functions of the first kind to solve fractional differential equations with variable coefficients. Then, we consider some applications of these results in order to…
We consider the fractional generalizations of Liouville equation. The normalization condition, phase volume, and average values are generalized for fractional case.The interpretation of fractional analog of phase space as a space with…
The equilibrium state of a system consisting of a large number of strongly interacting electrons can be characterized by its density operator. This gives a direct access to the ground-state energy or, at finite temperatures, to the free…
The new scheme of stochastic quantization is proposed. This quantization procedure is equivalent to the deformation of an algebra of observables in the manner of deformation quantization with an imaginary deformation parameter (the Planck…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
We propose a new type of cosmological model derived from the fractional variational principle when it is applied to the gravitational sector of action functional. In contrast to the fractional cosmological model developed earlier by the…
Formulation of quantum Hall dynamics using von Neumann lattice of guiding center coordinates is presented. A topological invariant expression of the Hall conductance is given and a new mean field theory of the fractional Hall effect based…
The Hamilton-Lagrange action principle for Relativistic Schr\"odinger Theory (RST) is converted to a variational principle (with constraints) for the stationary bound states. The groundstate energy is the minimally possible value of the…
The fractional Fourier transform (FrFT), which is a generalization of the Fourier transform, has become the focus of many research papers in recent years because of its applications in electrical engineering and optics. In this paper, we…
This paper presents a better approach to model an engineering problem in fractal-time space based on local fractional calculus. Some examples are given to elucidate to establish governing equations with local fractional derivative.
Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to…