The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and field theory. For the fractional linear oscillator the...

We derive the fractional generalization of the Ginzburg–Landau equation from the variational Euler–Lagrange equation for fractal media. To describe fractal media we use the fractional integrals considered as approximations of integrals on fractals. Some simple solutions of the...

Discrete nonlinear Schrödinger (DNLS) equation describes a chain of oscillators with nearest-neighbor interactions and a specific nonlinear term. We consider its modification with long-range interaction through a potential proportional to 1/l1+α with fractional α2 and l as a distance between...

Field equations with time and coordinate derivatives of noninteger order are derived from a stationary action principle for the cases of power-law memory function and long-range interaction in systems. The method is applied to obtain a fractional generalization of the Ginzburg–Landau and...

Using the generalized Kolmogorov–Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations, with averaging with respect to a fast variable, is used. The main assumption is that the...