Frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency-independent and frequency-squared dependent attenuations. The otherwise nonzero and nonsquare frequency dependency occurring in many cases of practical interest is thus often ...

The characterization of the global maximum of energy efficiency (EE) problems in wireless networks is a challenging problem due to its nonconvex nature in interference channels. The aim of this work is to develop a new and general framework to achieve globally optimal power control solutions. First, the hidden monotonic structure of the most common EE maximization problems is exploited jointly ...

A new LFM-signal detector formulated by the integration of the 4th-power modulus of the fractional Fourier transform is proposed. It has similar performance to the modulus square detector of Radon-ambiguity transform because of the equivalence relationship between them. But the new detector has much lower computational complexity in the case that the number of the searching angles is far less t...

A boundary value problem for a fractional power 0 < ε < 1 of the second-order elliptic operator is considered. The boundary value problem is singularly perturbed when ε→ 0. It is solved numerically using a time-dependent problem for a pseudo-parabolic equation. For the auxiliary Cauchy problem, the standard two-level schemes with weights are applied. The numerical results are presented for a mo...

A unified approach has been developed to study nonlinear dynamics of a 1D lattice of particles with long-range power-law interaction. Classical case is treated in the framework of the well-known FrenkelKontorova chain model. Qunatum dynamics is considered follow to Davydov’s approach to molecular excitons. In the continuum limit the problem is reduced to dynamical equations with fractional deri...

The acoustic wave attenuation is described by an experimentally established frequency power law in a variety of complex media, e.g., biological tissue, polymers, rocks, and rubber. Recent papers present a variety of acoustical fractional derivative wave equations that have the ability to model power-law attenuation. On the other hand, a multiple relaxation model is widely recognized as a physic...

We present a technique to improve the slow-light performance of a side-coupled integrated spaced sequence of resonators (SCISSOR) combined with a stimulated Brillouin scattering (SBS) gain medium in optical fibers. We evaluate device performance of SCISSOR-only and SCISSOR + SBS systems for different numbers of cascaded resonators from 1 to 70 using two different data fidelity metrics including...

Using the fact that extremum of variation of generalized action can lead to the fractional dynamics in the case of systems with long-range interaction and long-term memory function, we consider two different applications of the action principle: generalized Noether’s theorem and Hamiltonian type equations. In the first case, we derive conservation laws in the form of continuity equations that c...

Field equations with time and coordinate derivatives of noninteger order are derived from a stationary action principle for the cases of power-law memory function and long-range interaction in systems. The method is applied to obtain a fractional generalization of the Ginzburg–Landau and nonlinear Schrödinger equations. As another example, dynamical equations for particle chains with power-law ...

In this chapter, we present some emerging directions in bifurcation control in continuous-time dynamical systems. Specifically we discuss two unconventional bifurcation control problems: anti-control of bifurcations and nonsmooth bifurcation control. Anti-control of bifurcation means introducing a new bifurcation at desired location with preferred properties by appropriate control. Nonsmooth bi...