Related papers: Nonholonomic Constraints with Fractional Derivativ…
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…
We first introduce the generic versions of the fraction rules for monotonicity, i.e. the one that involves integrals known as the Gromov theorem and the other that involves derivatives known as L'H\^opital rule for monotonicity, which we…
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…
We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum in terms of solutions to Vlasov-type hierarchies. As a by-product we obtain the evolution of the density of particles in the…
We present a systematic derivation of the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) momentum composition law, dispersion relation, and momentum transformation laws, at…
This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…
Problems of calculus of variations with variable endpoints cannot be solved without transversality conditions. Here, we establish such type of conditions for fractional variational problems with the Caputo derivative. We consider: the…
We study fractional configurations in gravity theories and Lagrange mechanics. The approach is based on Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical…
In this note we study the application of generalized fractional operators to a particular class of nonstandard Lagrangians. These are typical of dissipative systems and the corresponding Euler-Lagrange and Hamilton equations are analyzed.…
This article provides an accessible introduction to fractional derivatives, a concept that extends classical calculus by allowing derivatives of non-integer order. It explores both the fundamental definitions and some of the most relevant…
We consider the compatibility of the equations of motion which follow from d'Alembert's principle in the case of a general autonomous non-holonomic mechanical system in N dimensions, with those equations which follow for the same system by…
Virtual constraints are invariant relations imposed on a control system via feedback as opposed to real physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints on the…
This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under nonholonomic constraints. For this…
The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining…
A new derivative, called deformable derivative, is introduced here which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach like that of ordinary one but with…
Two approximations, derived from continuous expansions of Riemann-Liouville fractional derivatives into series involving integer order derivatives, are studied. Using those series, one can formally transform any problem that contains…
We consider learning nonholonomic dynamical systems while discovering the constraints, and describe in detail the case of the rolling disk. A nonholonomic system is a system subject to nonholonomic constraints. Unlike holonomic constraints,…
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
The paper is devoted to the development of control procedures with a guide for conflict-controlled dynamical systems described by ordinary fractional differential equations with the Caputo derivative of an order $\alpha \in (0, 1).$ For the…
A version of fractional diffusion on bounded domains, subject to 'homogeneous Dirichlet boundary conditions' is derived from a kinetic transport model with homogeneous inflow boundary conditions. For nonconvex domains, the result differs…