We derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered alpha-stable processes. The tempering results in the existence of all moments of operational time. The subordination by the inverse tempered alpha-stable process provides diffusion (relaxation) that occupies an intermediate place between subdiffusion (Cole-Cole law) and normal diffusion (exponential law). Here we obtain explicitly the Fokker-Planck equation and the Cole-Davidson relaxation function. This model includes subdiffusion as a particular case.

We consider a fractional oscillator which is a generalization of the conventional linear oscillator in the framework of fractional calculus. It is interpreted as an ensemble average of ordinary harmonic oscillators governed by a stochastic time arrow. The intrinsic absorption of the fractional oscillator results from the full contribution of the harmonic oscillator ensemble: these oscillators differ a little from each other in frequency so that each response is compensated by an antiphase response of another harmonic oscillator. This allows one to draw a parallel in the dispersion analysis for media described by a fractional oscillator and an ensemble of ordinary harmonic oscillators with damping. The features of this analysis are discussed.

We consider the usual Langevin equation depending on an internal time. This parameter is substituted by a first passage time of a self-similar Markov process. Then the Gaussian process is parent, and the hitting time process is directing. The probability to find the resulting process at the real time is defined by the integral relationship between the probability densities of the parent and directing processes. The corresponding master equation becomes the fractional Fokker-Planck equation. We show that the resulting process has non-Markovian properties, all its moments are finite, the fluctuation-dissipation relation and the H-theorem hold.

We derive a general pattern of the nonexponential, two-power-law relaxation from the compound subordination theory of random processes applied to anomalous diffusion. The subordination approach is based on a coupling between the very large jumps in physical and operational times. It allows one to govern a scaling for small and large times independently.Here we obtain explicitly the relaxation function, the kinetic equation and the susceptibility expression applicable to the range of experimentally observed power-law exponents which cannot be interpreted by means of the commonly known Havriliak-Negami fitting function. We present a novel two-power relaxation law for this range in a convenient frequency-domain form and show its relationship to the Havriliak-Negami one.

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A time series of soft X-ray emission observed on 1974-2007 years (GOES) is analyzed. We show that in the periods of high solar activity 1977-1981, 1988-1992, 1999-2003 the energy statistics of soft X-ray solar flares for class M and C is well described by a FARIMA time series with Pareto innovations. The model is characterized by two effects. One of them is a long-range dependence (longterm memory), and another corresponds to heavy-tailed distributions. Their parameters are statistically stable enough during the periods. However, when the solar activity tends to minimum, they change essentially. We discuss possible causes of this evolution and suggest a statistical model for predicting the flare energy statistics.

The results of the first observations of Type IV bursts at frequencies 10-30 MHz are presented. These observations were carried out at radio telescopes UTR-2 (Kharkov, Ukraine) and URAN-2 (Poltava, Ukraine) during the period

International audienceThe current status of the large decameter radio telescope UTR-2 (Ukrainian T-shaped Radio telescope) together with its VLBI system called URAN is described in detail. By modernization of these instruments through implementation of novel versatile analog and digital devices as well as new observation techniques, the observational capabilities of UTR-2 have been substantially enhanced. The total effective area of UTR-2 and URAN arrays reaches 200 000 m2, with 24 MHz observational bandwidth (within the 8–32 MHz frequency range), spectral and temporal resolutions down to 4 kHz and 0.5 msec in dynamic spectrum mode or virtually unlimited in waveform mode. Depending on the spectral and temporal resolutions and confusion effects, the sensitivity of UTR-2 varies from a few Jy to a few mJy, and the angular resolution ranges from ~ 30 arcminutes (with a single antenna array) to a few arcseconds (in VLBI mode). In the framework of national and international research projects conducted in recent years, many new results on Solar system objects, the Galaxy and Metagalaxy have been obtained. In order to extend the observation frequency range to 8–80 MHz and enlarge the dimensions of the UTR-2 array, a new instrument – GURT (Giant Ukrainian Radio Telescope) – is now under construction. The radio telescope systems described herein can be used in synergy with other existing low-frequency arrays such as LOFAR, LWA, NenuFAR, as well as provide ground-based support for space-based instruments