Related papers: Fractional Calculus: Some Basic Problems in Contin…
This paper is devoted to study a class of stochastic Volterra equations associated with fractional Brownian motion. We first prove the Driver type integration by parts formula and the shift Harnack type inequalities. As a direct…
Recently, the research community has been exploring fractional calculus to address problems related to cosmology; in this approach, the gravitational action integral is altered, leading to a modified Friedmann equation, then the resulting…
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in…
The stochastic dynamics of small elastic objects in fluid are central to many important and emerging technologies. It is now possible to measure and use the higher modes of motion of elastic structures when driven by Brownian motion alone.…
In a first part the scope of classical thermodynamics and statistical mechanics is discussed in the broader context of formal dynamical systems, including computer programmes. In this context classical thermodynamics appears as a particular…
The time-fractional diffusion equation is considered, where the time derivative is either of Caputo or Riemann-Liouville type. The solution of a general initial-boundary value problem with time-dependent boundary conditions over bounded and…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative…
Recently, many interesting features of the hydrodynamically coupled motions of the Brownian particles in a viscous fluid have been reported which are impossible for the uncoupled motions of the similar particles. However, it is expected…
In this paper, a new fractional order generalization of the classical Windkessel arterial model is developed to describe the aortic input impedance as an assessment of the left ventricular after-load. The proposed models embeds…
In this paper we consider extensions of the gradient elasticity models proposed earlier by the second author to describe materials with fractional non-locality and fractality using the techniques developed recently by the first author. We…
The connection between fundamental interactions acting in molecules in a fluid and macroscopically measured properties, such as the viscosity between colloidal particles coated with polymers, is studied here. The role that hydrodynamic and…
There has been considerable recent study in "sub-diffusion" models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one…
This chapter presents some numerical methods to solve problems in the fractional calculus of variations and fractional optimal control. Although there are plenty of methods available in the literature, we concentrate mainly on approximating…
Modeling of wall-bounded turbulent flows is still an open problem in classical physics, with only modest progress made in the last few decades beyond the so-called `log law', which describes only the intermediate region in wall-bounded…
The non-Markovian continuous-time random walk model, featuring fat-tailed waiting times and narrow distributed displacements with a non-zero mean, is a well studied model for anomalous diffusion. Using an analytical approach, we recently…
The mathematical model of surfactant adsorption under mixed barrier-diffusion control is analyzed using techniques from fractional calculus. The kinetic models of Henry, Langmuir, Frumkin, Volmer and van der Waals are considered. First,…
We discuss a generalisation of fractional linear viscoelasticity based on Scarpi's approach to variable-order fractional calculus. After reviewing the general mathematical framework, we introduce the variable-order fractional Maxwell model…
In this paper, a multi-dimensional fractional wave equation that describes propagation of the damped waves is introduced and analyzed. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional…
We consider a system of multiscale stochastic differential equations whose slow component is drivenby a fractional Brownian motion with Hurst parameter H greater than 1/2. Under ergodic assumptions ensuring the applicability of the…