The linearly damped oscillator equation is considered with the damping term generalized to a Caputo fractional derivative. The order of the derivative being considered is 0 ≤ v ≤ 1. At the lower end v 0 the equation represents an undamped oscillator and at the upper end v 1 the ordinary linearly damped oscillator equation is recovered. A solution is found analytically, and a comparison with the...

We investigate the stability properties of strongly continuous semigroups generated by operators form $A-BB^\ast$, where $A$ is a generator contraction semigroup and $B$ possibly unbounded operator. Such systems arise naturally in study hyperbolic partial differential equations with damping on boundary or inside spatial domain. As our main results we present general sufficient conditions for no...

In this paper, we study the controllability of linear and nonlinear fractional damped dynamical systems, which involve fractional Caputo derivatives, with different order in finite dimensional spaces using the Mittag-Leffler matrix function and the iterative technique. A numerical example is provided to illustrate the theory.

Abstract Starting from kicked equations of motion with derivatives of non-integer orders, we obtain ‘fractional’ discrete maps. These maps are generalizations of wellknown universal, standard, dissipative, kicked damped rotator maps. The main property of the suggested fractional maps is a long-term memory. The memory effects in the fractional discrete maps mean that their present state evolutio...

This paper presents an analytical technique for the analysis of a stochastic dynamic system whose damping behavior is described by a fractional derivative of order 1/2. In this approach, an eigenvector expansion method proposed by Suarez and Shokooh is used to obtain the response of the system. The properties of Laplace transforms of convolution integrals are used to write a set of general Duha...

A 714-MHz RF system for the Accelerator Test Facility (ATF) damping ring has been constructed and commissioned. The RF system comprises two higherorder-mode (HOM) damped cavities, a 50-kW klystron, a WR-1150 waveguide network and low-level RF electronics. By using HOM-damped cavities, longitudinal and transverse coupled-bunch instabilities can be avoided even at a maximum beam current of 600mA....

The dynamic response of the railway under accelerated moving load using Dynamic Green Function is presented in this paper. For this purpose, an exact and direct modeling technique is introduced for the railway modeling as the damped Euler-Bernoulli beam on the partial Winkler foundation with arbitrary boundary conditions subjected to the moving load. The effects of the elastic coefficient of Wi...