Weighted S-Asymptotically omega-Periodic Solutions of a Class of Fractional Differential Equations

We study the existence of weighted S-asymptotically omega-periodic mild solutions for a class of abstract fractional differential equations of the form u' = partial derivative (alpha vertical bar 1)Au + f(t, u), 1 < alpha < 2, where A is a linear sectorial operator of negative type.

Emergent and reentrant fractional quantum Hall effect in trilayer systems in a tilted magnetic field

Magnetotransport measurements in triple-layer electron systems with high carrier density reveal fractional quantum Hall effect at total filling factors nu>2. With an in-plane magnetic field we are able to control the suppression of interlayer tunneling which causes a collapse of the integer quantum Hall plateaus at nu=2 and nu=4, and an emergence of fractional quantum Hall states with increasing tilt angles. The nu=4 state is replaced by three fractional quantum Hall states with denominator 3. The state nu=7/3 demonstrates reentrant behavior and the emergent state at nu=12/5 has a nonmonotonic behavior with increasing in-plane field. We attribute the observed fractional quantum Hall plateaus to correlated states in a trilayer system.

High-order fractional microwave-induced resistance oscillations in two-dimensional systems

We report on the observation of microwave-induced resistance oscillations associated with the fractional ratio n/m of the microwave irradiation frequency to the cyclotron frequency for m up to 8 in a two-dimensional electron system with high electron density. The features are quenched at high microwave frequencies independent of the fractional order m. We analyze temperature, power, and frequency dependencies of the magnetoresistance oscillations and discuss them in connection with existing theories.

Evaluating the efficiency of fractional integration parameter estimators

This article deals with the efficiency of fractional integration parameter estimators. This study was based on Monte Carlo experiments involving simulated stochastic processes with integration orders in the range]-1,1[. The evaluated estimation methods were classified into two groups: heuristics and semiparametric/maximum likelihood (ML). The study revealed that the comparative efficiency of the estimators, measured by the lesser mean squared error, depends on the stationary/non-stationary and persistency/anti-persistency conditions of the series. The ML estimator was shown to be superior for stationary persistent processes; the wavelet spectrum-based estimators were better for non-stationary mean reversible and invertible anti-persistent processes; the weighted periodogram-based estimator was shown to be superior for non-invertible anti-persistent processes.

On recent developments in the theory of abstract differential equations with fractional derivatives

This note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives. We show that the existence results in [Agarwal et al. (2009) [1], Belmekki and Benchohra (2010) [2], Darwish et al. (2009) [3], Hu et al. (2009) [4], Mophou and N`Guerekata (2009) [6,7], Mophou (2010) [8,9], Muslim (2009) [10], Pandey et al. (2009) [11], Rashid and El-Qaderi (2009) [12] and Tai and Wang (2009) [13]] are incorrect since the considered variation of constant formulas is not appropriate. In this note, we also consider a different approach to treat a general class of abstract fractional differential equations. (C) 2010 Elsevier Ltd. All rights reserved.

Fractional Photothermolysis for the Treatment of Hypertrophic Scars: Clinical Experience of Eight Cases

Hypertrophic scars are common problems and represent a challenging condition to treat. Fractional photothermolysis has been effective at resurfacing photodamaged skin, acne scars, and atrophic scars, but there are few reports on its use for hypertrophic scars. To evaluate the safety and efficacy of 1,550-nm erbium-doped fiber laser treatment of hypertrophic scars in eight patients. Eight patients (skin phototypes II-IV) with hypertrophic scars received monthly treatments with a 1,550-nm erbium-doped fiber laser. Energy settings ranged from 35 to 50 mJ, and eight to 10 passes were applied with treatment levels 6 to 8. An independent physician evaluator assessed the treatment response by comparing pre- and posttreatment clinical photographs using a quartile grading scale (grade 1, <= 25%=minimal to no improvement; grade 2, 26-50%=moderate improvement; grade 3, 51-75%=marked improvement; grade 4, > 75%=near total improvement. At four weeks after the last treatment session, a mean grade of 2.4 was achieved based on an independent physician`s clinical assessment. Improvement in pigmentation occurred in all hyperpigmented scars. Hypertrophic scars can be effectively and safely improved with 1,550-nm erbium-doped fiber laser treatment. The authors have indicated no significant interest with commercial supporters.

Elevated left and reduced right orbitomedial prefrontal fractional anisotropy in adults with bipolar disorder revealed by tract-based spatial statistics

Context Diffusion tensor imaging (DTI) studies in adults with bipolar disorder (BD) indicate altered white matter (WM) in the orbitomedial prefrontal cortex (OMPFC), potentially underlying abnormal prefrontal corticolimbic connectivity and mood dysregulatioin in BD. Objective: To use tract-based spatial statistics (TBSS) to examine VVM skeleton (ie, the most compact whole-brain WM) in subjects with BD vs healthy control subjects. Design: Cross-sectional, case-control, whole-brain DTI using TBSS. Setting: University research institute. Participants: Fifty-six individuals, 31 having a DSM-IV diagnosis of BD type 1 (mean age, 35.9 years [age range, 24-52 years]) and 25 controls (mean age, 29.5 years [age range, 19-52 years]). Main Outcome Measures: Fractional anisotropy (FA) longitudinal and radial diffusivities in subjects with BD vs controls (covarying for age) and their relationships with clinical and demographic variables. Results: Subjects with BD vs controls had significantly greater FA (t > 3.0, P <=.05 corrected) in the left uncinate fasciculus (reduced radial diffusivity distally and increased longitudinal diffusivity centrally), left optic radiation (increased longitudinal diffusivity), and right anterothalamic radiation (no significant diffusivity change). Subjects with BD vs controls had significantly reduced FA (t > 3.0, P <=.05 corrected) in the right uncinate fasciculus (greater radial diffusivity). Among subjects with BD, significant negative correlations (P <.01) were found between age and FA in bilateral uncinate fasciculi and in the right anterothalamic radiation, as well as between medication load and FA in the left optic radiation. Decreased FA (P <.01) was observed in the left optic radiation and in the right anterothalamic radiation among subjects with BD taking vs those not taking mood stabilizers, as well as in the left optic radiation among depressed vs remitted subjects with BD. Subjects having BD with vs without lifetime alcohol or other drug abuse had significantly decreased FA in the left uncinate fasciculus. Conclusions: To our knowledge, this is the first study to use TBSS to examine WM in subjects with BD. Subjects with BD vs controls showed greater WM FA in the left OMPFC that diminished with age and with alcohol or other drug abuse, as well as reduced WM FA in the right OMPFC. Mood stabilizers and depressed episode reduced WM FA in left-sided sensory visual processing regions among subjects with BD. Abnormal right vs left asymmetry in FA in OMPFC WM among subjects with BD, likely reflecting increased proportions of left-sided longitudinally aligned and right-sided obliquely aligned myelinated fibers, may represent a biologic mechanism for mood dysregulation in BD.

A Pitch Control Malfunction Analysis for Wind Turbines with Permanent Magnet Synchronous Generator and Full-power Converters: Proportional Integral Versus Fractional-order Controllers

A transient analysis for two full-power converter wind turbines equipped with a permanent magnet synchronous generator is studied in this article, taking into consideration, as a new contribution to earlier studies, a pitch control malfunction. The two full-power converters considered are, respectively, a two-level and a multi-level converter. Moreover, a novel control strategy based on fractional-order controllers for wind turbines is studied. Simulation results are presented; conclusions are in favor of the novel control strategy, improving the quality of the energy injected into the electric grid.

Fractional-order control and simulation of wind energy systems with PMSG/full-power converter topology

This paper presents a new integrated model for the simulation of wind energy systems. The proposed model is more realistic and accurate, considering a variable-speed wind turbine, two-mass rotor, permanent magnet synchronous generator (PMSG), different power converter topologies, and filters. Additionally, a new control strategy is proposed for the variable-speed operation of wind turbines with PMSG/full-power converter topology, based on fractional-order controllers. Comprehensive simulation studies are carried out with matrix and multilevel power converter topologies, in order to adequately assert the system performance in what regards the quality of the energy injected into the electric grid. Finally, conclusions are duly drawn.

A DC-DC Step-Up mu-Power Converter for Energy Harvesting Applications, Using Maximum Power PointTracking, Based on Fractional Open Circuit Voltage

A DC-DC step-up micro power converter for solar energy harvesting applications is presented. The circuit is based on a switched-capacitorvoltage tripler architecture with MOSFET capacitors, which results in an, area approximately eight times smaller than using MiM capacitors for the 0.131mu m CMOS technology. In order to compensate for the loss of efficiency, due to the larger parasitic capacitances, a charge reutilization scheme is employed. The circuit is self-clocked, using a phase controller designed specifically to work with an amorphous silicon solar cell, in order to obtain themaximum available power from the cell. This will be done by tracking its maximum power point (MPPT) using the fractional open circuit voltage method. Electrical simulations of the circuit, together with an equivalent electrical model of an amorphous silicon solar cell, show that the circuit can deliver apower of 1132 mu W to the load, corresponding to a maximum efficiency of 66.81%.

Wind turbines equipped with fractional-order controllers: Stress on the mechanical drive train due to a converter control malfunction

This paper is on variable-speed wind turbines with permanent magnet synchronous generator (PMSG). Three different drive train mass models and three different topologies for the power-electronic converters are considered. The three different topologies considered are respectively a matrix, a two-level and a multilevel converter. A novel control strategy, based on fractional-order controllers, is proposed for the wind turbines. Simulation results are presented to illustrate the behaviour of the wind turbines during a converter control malfunction, considering the fractional-order controllers. Finally, conclusions are duly drawn. Copyright (C) 2010 John Wiley & Sons, Ltd.

Fractional dynamics in DNA

This paper addresses the DNA code analysis in the perspective of dynamics and fractional calculus. Several mathematical tools are selected to establish a quantitative method without distorting the alphabet represented by the sequence of DNA bases. The association of Gray code, Fourier transform and fractional calculus leads to a categorical representation of species and chromosomes.

On local fractional continuous wavelet transform

We introduce a new wavelet transform within the framework of the local fractional calculus. An illustrative example of local fractional wavelet transform is also presented.

Fractional dynamics and MDS visualization of earthquake phenomena

This paper analyses earthquake data in the perspective of dynamical systems and fractional calculus (FC). This new standpoint uses Multidimensional Scaling (MDS) as a powerful clustering and visualization tool. FC extends the concepts of integrals and derivatives to non-integer and complex orders. MDS is a technique that produces spatial or geometric representations of complex objects, such that those objects that are perceived to be similar in some sense are placed on the MDS maps forming clusters. In this study, over three million seismic occurrences, covering the period from January 1, 1904 up to March 14, 2012 are analysed. The events are characterized by their magnitude and spatiotemporal distributions and are divided into fifty groups, according to the Flinn–Engdahl (F–E) seismic regions of Earth. Several correlation indices are proposed to quantify the similarities among regions. MDS maps are proven as an intuitive and useful visual representation of the complex relationships that are present among seismic events, which may not be perceived on traditional geographic maps. Therefore, MDS constitutes a valid alternative to classic visualization tools for understanding the global behaviour of earthquakes.

Fractional model for malaria transmission under control strategies

We study a fractional model for malaria transmission under control strategies.Weconsider the integer order model proposed by Chiyaka et al. (2008) in [15] and modify it to become a fractional order model. We study numerically the model for variation of the values of the fractional derivative and of the parameter that models personal protection, b. From observation of the figures we conclude that as b is increased from 0 to 1 there is a corresponding decrease in the number of infectious humans and infectious mosquitoes, for all values of α. This means that this result is invariant for variation of fractional derivative, in the values tested. These results are in agreement with those obtained in Chiyaka et al.(2008) [15] for α = 1.0 and suggest that our fractional model is epidemiologically wellposed.