Black box modeling of diffusion processes can be performed by fractional models. The simulation of these particular models is based on a new fractional integrator, with limited spectral range. Parameter estimation of this class of systems is performed by an OE identification technique. This paper presents the application of this new methodology to the modeling of different diffusive systems dea...

the aim of this paper is to model thermal flux versus temperature in an aluminum rod. The objective is to check whether a theoretical model applies to experimental data and then to investigate some more effective fractional models from black box identification. For this particular system, it is shown that fractional models are more suitable than rational ones, since they require fewer parameter...

We study static and radially symmetric black holes in the multi-fractional theories of gravity with q-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length [Formula: see text]. In the q-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black ...

We study thermodynamic state-space geometry of the black holes in string theory and M -theory. For a large number of microstates, we analyze the intrinsic state-space geometry for (i) extremal and non-extremal black branes in string theory, (ii) multi-centered black brane configurations, (iv) small black holes with fractional branes, and (v) fuzzy rings in the setup of Mathur’s fuzzballs and su...

We compute the entropy of systems of quantum particles satisfying the fractional exclusion statistics in the space-time of 2+1 dimensional black hole by using the brick-wall method. We show that the entropy of each effective quantum field theory with a Planck scale ultraviolet cutoff obeys the area law, irrespective of the angular momentum of the black hole and the statistics interpolating betw...

Many approaches to a semiclassical description of gravity lead to an integer black hole entropy. In four dimensions this implies that the Schwarzschild radius obeys a formula which describes the distance covered by a Brownian random walk. For the higher-dimensional Schwarzschild-Tangherlini black hole, its radius relates similarly to a fractional Brownian walk. We propose a possible microscopic...

It has been proposed that the arbitrage possibility in the fractional Black–Scholes model depends on the definition of the stochastic integral. More precisely, if one uses the Wick– Itô–Skorohod integral one obtains an arbitrage-free model. However, this integral does not allow economical interpretation. On the other hand it is easy to give arbitrage examples in continuous time trading with sel...

Three main types of low-frequency quasi-periodic oscillations (LFQPOs) have been observed in Black Hole Candidates. We re-analyzed RXTE data of the bright systems XTE J1859+226, XTE J1550-564 and GX 339-4, which show all three of them. We review the main properties of these LFQPOs and show that they follow a well-defined correlation in a fractional rms vs. softness diagram. We show that the fre...

The characteristics of black-hole X-ray binaries can be used to obtain information about their evolutionary history and the process of black-hole formation. In this paper I focus on systems with donor masses lower than the inferred black-hole masses. Current models for the evolution of hydrogen-rich, massive stars and of helium stars losing mass in a wind cannot explain the current sample of bl...