In this paper fractional generalization of Liouville equation is considered. We derive fractional analog of normalization condition for distribution function. Fractional generalization of the Liouville equation for dissipative and Hamiltonian systems was derived from the fractional normalization condition. This condition is considered as a normalization condition for systems in fractional phase...

In this article, we consider dissipative Sturm–Liouville operators in the limit-circle case on time scales. Then, using the Livšic’s Theorem, we prove the completeness of the system of root vectors for dissipative Sturm–Liouville operators. 2013 Elsevier Inc. All rights reserved.

We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions, one being affinely dependent on the eigen-parameter. We give sufficient conditions under which a basis of each root subspace for this Sturm-Liouville problem can be selected so that the union of all these bases constitutes a Riesz basis of a corresponding weighted Hilbert space.

In this manuscript, a numerical technique is presented for finding the eigenvalues of the regular Sturm-Liouville problems. The Chebyshev cardinal functions are used to approximate the eigenvalues of a regular Sturm-Liouville problem with Dirichlet boundary conditions. These functions defined by the Chebyshev function of the first kind. By using the operational matrix of derivative the problem ...

The globalization of some local structures as the complex Liouville vector field, complex Liouville 1-form, totally singular complex Hamiltonians and complex nonlinear connection on holomorphic Lagrangian fibrations is studied. Also, we give a new characterization of equivalence of two holomorphic Lagrangian foliations. The notions are introduced here by analogy with the real case, see [16, 17,...

Motivated by the supersymmetric extension of Liouville theory in the recent physics literature, we couple the standard Liouville functional with a spinor field term. The resulting functional is conformally invariant. We study geometric and analytic aspects of the resulting Euler-Lagrange equations, culminating in a blow up analysis.

A method of defining the complex structure(i.e. moduli) for dynamically triangulated(DT) surfaces with torus topology is proposed. Distribution of the moduli parameter is measured numerically and compared with the Liouville theory for the surface coupled to c = 0, 1 and 2 matter. Equivalence between the dynamical triangulation and the Liouville theory is established in terms of the complex stru...

The Liouville equation of a two-level atom coupled to a degenerate bimodal lossy cavity is unitarily and exactly reduced to two uncoupled Liouville equations. The first one describes a dissipative Jaynes-Cummings model and the other one a damped harmonic oscillator. Advantages related to the reduction method are discussed. 42.50.-p, 42.50.Ct, 42.60.Da, 32.80.-t Typeset using REVTEX 2

Here we state the main properties of the Caputo, Riemann-Liouville and the Caputo via Riemann-Liouville fractional derivatives and give some general notes on these properties. Some properties given in some recent literatures and used to solve fractional nonlinear partial differential equations will be proved that they are incorrect by giving some counter examples.

The classification of the coadjoint orbits of the Virasoro algebra is reviewed and is then applied to analyze the so-called global Liouville equation. The review is selfcontained, elementary and is tailor-made for the application. It is well-known that the Liouville equation for a smooth, real field φ under periodic boundary condition is a reduction of the SL(2,R) WZNW model on the cylinder, wh...