2006 · 242 citations · 15 references
Natural SciencesMathematicsMechatronics EngineeringDifferential EquationsDynamical SystemsSystem DynamicsApproximation AlgorithmsApproximation MethodsNumerical AlgorithmsNumerical AnalysisNumerical Methods For Differential EquationsAnalytic ApproximationsDynamic Systems ApproachFractional Differential Equations
Many real world systems, including smart mechatronics systems, can be better characterized by dynamic systems of non-integer order. Using non-integer order or fractional order calculus, fractional order systems can be modeled more authentically. Due to the nature of the infinite dimensional model, proper approximations to fractional order differentiator (s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">alpha</sup> , alpha isin Ropf) are fundamentally important. This paper contributed a new approximation scheme which is an extension of the well-established Oustaloup's approximation method. The benefits from using the proposed scheme are illustrated by numerical examples in both time and frequency domains
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Fractional Calculus in Bioengineering
Bruce J. West · Journal of Statistical Physics · 2007 · 2K citations