13 research outputs found
Transform of Riccati equation of constant coefficients through fractional procedure
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 expressed as a power of the independent variable which is of the same
order as the order of the applied fractional derivative. We provide the
solutions of the modified equation and employ the results for the case of the
cosmological Riccati equation of FRW barotropic cosmologies that has been
recently introduced by FaraoniComment: 7 pages, 2 figure
Fractional Klein-Kramers equation for superdiffusive transport: normal versus anomalous time evolution in a differential L{\'e}vy walk model
We introduce a fractional Klein-Kramers equation which describes
sub-ballistic superdiffusion in phase space in the presence of a
space-dependent external force field. This equation defines the differential
L{\'e}vy walk model whose solution is shown to be non-negative. In the velocity
coordinate, the probability density relaxes in Mittag-Leffler fashion towards
the Maxwell distribution whereas in the space coordinate, no stationary
solution exists and the temporal evolution of moments exhibits a competition
between Brownian and anomalous contributions.Comment: 4 pages, REVTe
Fractional Generalization of Quantum Markovian Master Equation
We prove a generalization of the quantum Markovian equation for observables.
In this generalized equation, we use superoperators that are fractional powers
of completely dissipative superoperators. We prove that the suggested
superoperators are infinitesimal generators of completely positive semigroups
and describe the properties of this semigroup. We solve the proposed fractional
quantum Markovian equation for the harmonic oscillator with linear friction. A
fractional power of the Markovian superoperator can be considered a parameter
describing a measure of "screening" of the environment of the quantum system:
the environmental influence on the system is absent for , the
environment completely influences the system for , and we have a
powerlike environmental influence for .Comment: 25 pages, LaTe
Global existence of solutions for a fractional Caputo nonlocal thermistor problem
We begin by proving a local existence result for a fractional Caputo nonlocal
thermistor problem. Then additional existence and continuation theorems are
obtained, ensuring global existence of solutions