Related papers: Deriving friction force using fractional calculus
In multi-fluid description of heavy-ion collisions, the primary scatterings and particle production are described in terms of interaction between fluids, so called friction. These friction terms can be derived from kinetic theory, but they…
Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered ``anomalous''. It is often used when traditional integer derivatives models fail to represent cases…
We introduce a discrete-time fractional calculus of variations on the time scale $h\mathbb{Z}$, $h > 0$. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and…
The dynamical friction force experienced by a body moving at relativistic speed in a gaseous medium is examined. This force, which arises due to the gravitational interaction of the body with its own gravitationally-induced wake, is…
The dynamic frictional force between solid surfaces in relative motion differs from the static force needed to initiate motion, but this distinction is not usually thought to occur for liquid drops moving on a solid. Recent experiments…
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…
A set of brackets for classical dissipative systems, subject to external random forces, are derived. The method is inspired to the old procedure found by Peierls, for deriving the canonical brackets of conservative systems, starting from an…
Methods from the geometry of nonholonomic manifolds and Lagrange-Finsler spaces are applied in fractional calculus with Caputo derivatives and for elaborating models of fractional gravity and fractional Lagrange mechanics. The geometric…
Fractional derivatives are nonlocal differential operators of real order that often appear in models of anomalous diffusion and a variety of nonlocal phenomena. Recently, a version of the Schr\"odinger Equation containing a fractional…
A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle,…
While there are a number of models that tackle the problem of calculating friction forces on the atomic level, providing a completely parameter-free approach remains a challenge. Here we present a quasi-static model to obtain an…
In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of…
In the present article, an approach to find the exact solution of the fractional Fokker-Planck equation is presented. It is based on transforming it to a system of first-order partial differential equation via Hopf transformation, together…
The friction force, friction coefficients and the effects on the dynamics of particles, bodies and systems, are fundamental themes in university physics of the first cycles and also in general physics courses of upper secondary education in…
Fractional kinetic theory plays a vital role in describing anomalous diffusion in terms of complex dynamics generating semi-Markovian processes. Recently, the variational principle and associated Levy Ansatz have been proposed in order to…
We develop the theory of fractional gradient flows: an evolution aimed at the minimization of a convex, l.s.c.~energy, with memory effects. This memory is characterized by the fact that the negative of the (sub)gradient of the energy equals…
Thermal fluctuations in non-equilibrium steady states generically lead to power law decay of correlations for conserved quantities. Embedded bodies which constrain fluctuations in turn experience fluctuation induced forces. We compute these…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.
We give a proper fractional extension of the classical calculus of variations by considering variational functionals with a Lagrangian depending on a combined Caputo fractional derivative and the classical derivative. Euler-Lagrange…