Related papers: Fractional Hamiltonian analysis of higher order de…

Introducing a perturbative definition, phase space path integrals can be calculated without slicing. This leads to a short-time expansion of the quantum-mechanical path amplitude, or a high-temperature expansion of the unnormalized density…

The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.

The Liouville and first Bogoliubov hierarchy equations with derivatives of noninteger order are derived. The fractional Liouville equation is obtained from the conservation of probability to find a system in a fractional volume element.…

The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent.

We carry out the extension of the Ostrogradski method to relativistic field theories. Higher-derivative Lagrangians reduce to second differential-order with one explicit independent field for each degree of freedom. We consider a…

By means of a simple scalar field theory it is demonstrated that the Lagrange formalism and Ostrogradsky's Hamilton formalism in the presence of higher derivatives, in general, do not lead to the same results. While the two approaches are…

In this paper, we use the fractional calculus to discuss the fractional mechanics, where the time derivative is replaced with the fractional derivative of order $\nu$. We deal with the motion of a body in a resisting medium where the…

We introduce a new fractional oscillator process which can be obtained as solution of a stochastic differential equation with two fractional orders. Basic properties such as fractal dimension and short range dependence of the process are…

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…

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…

Cosmological models of a scalar field with dynamical equations containing fractional derivatives or derived from the Einstein-Hilbert action of fractional order, are constructed. A number of exact solutions to those equations of fractional…

We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar…

Fractional derivatives are generalization to classical integer-order derivatives. The rules which are true for classical derivative need not hold for the fractional derivatives, for example, we cannot simply add the fractional orders…

Based on a simple observation that a classical second order differential equation may be decomposed into a set of two first order equations, we introduce a Hamiltonian framework to quantize the damped systems. In particular, we analyze the…

Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation…

We consider a class of Lagrangians that depend not only on some configurational variables and their first time derivatives, but also on second time derivatives, thereby leading to fourth-order evolution equations. The proposed higher-order…

We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered. We describe the stationary states of these…

The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach it has the following advantages: (i) the Lagrangian, when expressed in terms of new variables…

Fractional mechanics describes both conservative and non-conservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics the…

The problems that are connected with Lagrangians which depend on higher order derivatives (namely additional degrees of freedom, unbound energy from below, etc.) are absent if effective Lagrangians are considered because the equations of…