Journal ArticleDOI
Fractional-Order Sinusoidal Oscillators: Design Procedure and Practical Examples
TLDR
The Barhkausen condition for a linear noninteger-order (fractional-order) dynamical system to oscillate is derived and the oscillation condition and oscillation frequency of some famous integer-order sinusoidal oscillators can be obtained as special cases from general equations governing their fractional- order counterparts.Abstract:
Sinusoidal oscillators are known to be realized using dynamical systems of second-order or higher. Here we derive the Barhkausen condition for a linear noninteger-order (fractional-order) dynamical system to oscillate. We show that the oscillation condition and oscillation frequency of some famous integer-order sinusoidal oscillators can be obtained as special cases from general equations governing their fractional-order counterparts. Examples including fractional-order Wien oscillators, Colpitts oscillator, phase-shift oscillator and LC tank resonator are given supported by numerical and PSpice simulations.read more
Citations
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Journal ArticleDOI
Fractional-order circuits and systems: An emerging interdisciplinary research area
TL;DR: A recent article published in this magazine has labeled fractional-order continuous-time systems as the "21st century systems" and highlighted specific problems which need to be addressed particularly by electrical engineers.
Journal ArticleDOI
On the stability of linear systems with fractional-order elements
TL;DR: In this paper, the stability of linear integer-order circuits with one fractional element, two fractional elements of the same order or two fractions of different order is studied, and a general procedure for studying the system with many fractional components is also given.
Journal ArticleDOI
On the generalization of second-order filters to the fractional-order domain
TL;DR: This work considers here the case where a filter is constructed using two fractional-order capacitors both of the same order α, and shows for the first time experimental results using the fractional capacitive probe described in Ref. 1.
Journal ArticleDOI
RC models of a constant phase element
Juraj Valsa,Jiri Vlach +1 more
TL;DR: Three models of a constant-phase element consisting of passive R and C components are described, which can be used for practical realization of fractional analog differentiators and integrators, fractional oscillators, chaotic networks or for analog simulation of fractionsal control systems.
Journal ArticleDOI
Fractional Order Butterworth Filter: Active and Passive Realizations
TL;DR: This paper presents a general procedure to obtain Butterworth filter specifications in the fractional-order domain where an infinite number of relationships could be obtained due to the extra independent fractional -order parameters which increase the filter degrees-of-freedom.
References
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Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Book
Fractional Integrals and Derivatives: Theory and Applications
TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.
Book
The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order
Keith B. Oldham,Jerome Spanier +1 more
TL;DR: In the beginning, when having significantly cash, why don't you attempt to acquire something basic in the beginning? That's something that will guide you to understand even more in the region of the globe, experience, some places, history, amusement, and a lot more as discussed by the authors.
Journal ArticleDOI
Analysis of Fractional Differential Equations
Kai Diethelm,Neville J. Ford +1 more
TL;DR: In this paper, the authors discuss existence, uniqueness, and structural stability of solutions of nonlinear differential equations of fractional order, and investigate the dependence of the solution on the order of the differential equation and on the initial condition.
Proceedings Article
Stability results for fractional differential equations with applications to control processing
TL;DR: In this article, stability results for finite-dimensional linear fractional differential systems in state-space form are given for both internal and external stability, and the main qualitative result is that stabilities are guaranteed iff the roots of some polynomial lie outside the closed angular sector.