Related papers: Nonholonomic Constraints with Fractional Derivativ…
We consider a nonlinear parabolic equation of fractional order in space and propose its numerical discretization. The fractional derivative is defined through a functional analytic setting, rather than the traditional definition of…
Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…
A methodology for deriving dual variational principles for the classical Newtonian mechanics of mass points in the presence of applied forces, interaction forces, and constraints, all with a general dependence on particle velocities and…
We demonstrate that the complete factorization of equations of motion into first-order differential equations can be obtained for real and complex scalar field theories with non-canonical dynamics.
In the present work, we formulate a necessary condition for functionals with Lagrangians depending on fractional derivatives of differentiable functions to possess an extremum. The Euler-Lagrange equation we obtained generalizes previously…
Employing a suitable nonlinear Lagrange functional, we derive generalized Hamilton-Jacobi equations for dynamical systems subject to linear velocity constraints. As long as a solution of the generalized Hamilton-Jacobi equation exists, the…
Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…
Lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers. The geometry, solutions, symmetries and constants of motion of such equations are…
The least action principle seems not to lead to equations describing the motion consistent with the physical behavior for nonholonomic constrains. Here an answer to this question in proposed.
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…
Fractional derivatives are generalization to classical integer-order derivatives. The rules which are true for classical derivative need not hold for the fractional derivatives, for example, we cannot simply add the fractional orders…
Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…
(Draft 3) A generalized differential operator on the real line is defined by means of a limiting process. These generalized derivatives include, as a special case, the classical derivative and current studies of fractional differential…
The aim of this paper is to study certain problems of calculus of variations, that are dependent upon a Lagrange function on a Caputo-type fractional derivative. This type of fractional operator is a generalization of the Caputo and the…
In the comparison of nonholonomic mechanics and constrained variational mechanics, invariant affine subbundles arise in the determination of the initial conditions where the two methods yield the same trajectories. Motivated by this,…
Using kicked differential equations of motion with derivatives of noninteger orders, we obtain generalizations of the dissipative standard map. The main property of these generalized maps, which are called fractional maps, is long-term…
The construction of stochastic solutions for nonlinear partial differential equations is a powerful method to obtain new exact results and to develop efficient numerical algorithms, in particular when domain decomposition techniques are…
Variational principles play a central role in classical mechanics, providing compact formulations of dynamics and direct access to conserved quantities. While holonomic systems admit well-known action formulations, non-holonomic systems --…
An investigation of classical fields with fractional derivatives is presented using the fractional Hamiltonian formulation. The fractional Hamilton's equations are obtained for two classical field examples. The formulation presented and the…
We study fractional variational problems of Herglotz type of variable order. Necessary optimality conditions, described by fractional differential equations depending on a combined Caputo fractional derivative of variable order, are proved.…