Related papers: Deriving friction force using fractional calculus
Transport equations with a nonlocal velocity field have been introduced as a continuum model for interacting particle systems arising in physics, chemistry and biology. Fractional time derivatives, given by convolution integrals of the…
Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to…
The equation of motion for the expectation value of a scalar quantum field does not have the local form that is commonly assumed in studies of inflationary cosmology. We have recently argued that the true, temporally non-local equation of…
A mechanical covariant equation is introduced which retains all the effectingness of the Lagrange equation while being able to describe in a unified way other phenomena including friction, non-holonomic constraints and energy radiation…
In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of…
Field equations with time and coordinates derivatives of noninteger order are derived from stationary action principle for the cases of power-law memory function and long-range interaction in systems. The method is applied to obtain a…
The time-fractional convection-diffusion equation is performed by Lie symmetry analysis method which involves the Riemann-Liouville time-fractional derivative of the order $\alpha\in(0,2)$. In eight cases, the symmetries are obtained and…
Fractional variational approach has gained much attention in recent years. There are famous fractional derivatives such as Caputo derivative, Riesz derivative and Riemann-Liouville derivative. Several versions of fractional variational…
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…
In this paper, we resort to the Laplace transform method in order to show its efficiency when approaching some types of fractional differential equations. In particular, we present some applications of such methods when applied to possible…
The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent.
Fractional variation is defined as the limit of the difference quotient of the increments of a function and its argument raised to a fractional power. Fractional velocity can be suitable for characterizing singular behavior of derivatives…
Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of…
A modification of Coulomb's law of friction uses a variable coefficient of friction that depends on a power law in the energy of mechanical oscillation. Through the use of three different exponents: 0, 1/2 and 1; all commonly encountered…
We consider geometric variational problems for a functional defined on a curve in three-dimensional space. The functional is assumed to be written in a form invariant under the group of Euclidean motions. We present the Euler-Lagrange…
The equation of motion for test particles in $f(R)$ modified theories of gravity is derived. By considering an explicit coupling between an arbitrary function of the scalar curvature, $R$, and the Lagrangian density of matter, it is shown…
Dissipative Lagrangians and Hamiltonians having Coulomb, viscous and quadratic damping,together with gravitational and elastic terms are presented for a formalism that preserves the Hamiltonian as a constant of the motion. Their derivations…
We present a conundrum that results from the imprecise use of notation for partial derivatives. Taking an example from mechanics, we show that lack of proper care in representing partial derivatives in Lagrangian and Hamiltonian…
We consider two spin-1/2 particles with isotropic Heisenberg interaction, as the working substance of a quantum heat engine. We observe a frictional effect on the adiabatic branches of the heat cycle, which arises due to an inhomogeneous…
In cosmological first-order phase transitions, the microscopic interaction of the phase transition fronts with non-equilibrium plasma particles manifests itself macroscopically as friction forces. In general, it is a nontrivial problem to…