TY - CHAP

T1 - Fractional linear shift-invariant systems

AU - Ortigueira, Manuel Duarte

PY - 2011

Y1 - 2011

N2 - The applications of Fractional Calculus to physics and engineering are not recent: the beginning of the application to viscosity dates back to the thirties in the past century. During the last 20 years the application domains of fractional calculus increased significantly: seismic analysis (Koh and Kelly, 1990), dynamics of motor and premotor neurones of the oculomotor systems, viscous damping, electric fractal networks, fractional order sinusoidal oscillators and, more recently, control, and robotics. One of the areas where such can be verified is the Biomedical Engineering. The now classic fractional Brownian motion (fBm) modeling is an application of the fractional calculus. We define a fractional noise that is obtained through a fractional derivative of white noise. The fBm is an integral of the fractional noise.

AB - The applications of Fractional Calculus to physics and engineering are not recent: the beginning of the application to viscosity dates back to the thirties in the past century. During the last 20 years the application domains of fractional calculus increased significantly: seismic analysis (Koh and Kelly, 1990), dynamics of motor and premotor neurones of the oculomotor systems, viscous damping, electric fractal networks, fractional order sinusoidal oscillators and, more recently, control, and robotics. One of the areas where such can be verified is the Biomedical Engineering. The now classic fractional Brownian motion (fBm) modeling is an application of the fractional calculus. We define a fractional noise that is obtained through a fractional derivative of white noise. The fBm is an integral of the fractional noise.

UR - http://www.scopus.com/inward/record.url?scp=79959702763&partnerID=8YFLogxK

U2 - 10.1007/978-94-007-0747-4_4

DO - 10.1007/978-94-007-0747-4_4

M3 - Chapter

AN - SCOPUS:79959702763

SN - 9789400707467

T3 - Lecture Notes in Electrical Engineering

SP - 71

EP - 99

BT - Fractional Calculus for Scientists and Engineers

ER -