相关论文: Fractional Dynamics of Systems with Long-Range Spa…
We introduce a fractional Fokker-Planck equation with a temporal power-law dependence on the drift force fields. For this case, the moments of the tracer from the force-force correlation in terms of the time-dependent drift force fields are…
In the realm of complexity, it is argued that adequate modeling of TeV-physics demands an approach based on fractal operators and fractional calculus (FC). Non-local theories and memory effects are connected to complexity and the FC. The…
We analyze the quantum dynamics of the fractional-time Jaynes-Cummings model using a recent unitary framework for the fractional-time Schr\"odinger equation. We examine how the fractional derivative order $\alpha$ influences non-classical…
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…
We consider the linear response of systems modelled by continuous-time random walks (CTRW) and by fractional Fokker-Planck equations under the influence of time-dependent external fields. We calculate the corresponding response functions…
We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the…
Long and short memory in economic processes is usually described by the so-called discrete fractional differencing and fractional integration. We prove that the discrete fractional differencing and integration are the Grunwald-Letnikov…
One-dimensional Ginzburg-Landau equations with derivatives of noninteger order are considered. Using psi-series with fractional powers, the solution of the fractional Ginzburg-Landau (FGL) equation is derived. The leading-order behaviours…
Using the molecular dynamics method, we examine a discrete deterministic model for the motion of spherical particles in three-dimensional space. The model takes into account multiparticle collisions in arbitrary forms. Using fractional…
Front dynamics modeled by a reaction-diffusion equation are studied under the influence of spatio-temporal structured noises. An effective deterministic model is analytical derived where the noise parameters, intensity, correlation time and…
A fractional variational principle was derived in order to be used with lagrangians containing fractional derivatives of order 1/2. By forcing the action associated to this type of lagrangian to be stationary, a modified fractional…
Fractional electromagnetic field theory describes electromagnetic wave propagation through the complex, nonlocal, dissipative, fractal and also recent artificially engineered materials know as fractional metamaterials. In this theory using…
Acceleration-induced nonlocality and the corresponding Lorentz-invariant nonlocal field equations of accelerated systems in Minkowski spacetime are discussed. Under physically reasonable conditions, the nonlocal equation of motion of the…
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…
In the present work, by taking advantage of a so-called practical limitation of fractional derivatives, namely, the absence of a simple chain and Leibniz's rules, we proposed a generalized fractional calculus of variation where the…
Levy flights and fractional Brownian motion (fBm) have become exemplars of the heavy tailed jumps and long-ranged memory seen in space physics and elsewhere. Natural time series frequently combine both effects, and Linear Fractional Stable…
It is well-known that the transition function of the Ornstein-Uhlenbeck process solves the Fokker-Planck equation. This standard setting has been recently generalized in different directions, for example, by considering the so-called…
We consider the fractional generalization of nonholonomic constraints defined by equations with fractional derivatives and provide some examples. The corresponding equations of motion are derived using variational principle.
In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has…
A fractional generalization of variations is used to define a stability of non-integer order. Fractional variational derivatives are suggested to describe the properties of dynamical systems at fractional perturbations. We formulate…