Fractional Calculus - Gauge-institute.org
Fractional Calculus - Gauge-institute.org
Fractional Calculus - Gauge-institute.org
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<strong>Gauge</strong> Institute Journal, Volume 5, No 1, February 2009H. Vic DannonThe meaning of order n +1<strong>Fractional</strong> Derivative follows from21 1 12 2 + 1 2n + n n ( − )D f( x) = D D f( x) = D F ( x).3.6 The Applicability of the <strong>Fractional</strong> <strong>Calculus</strong>The meaning of the <strong>Fractional</strong> Derivative enables us to evaluatethe applicability of the <strong>Fractional</strong> <strong>Calculus</strong> in simple terms:The <strong>Fractional</strong> Derivative of order 1 2may be useful in a modelthat involves the Convolution Transform12( − )F ( x). That is,If you can see the Convolution Transform underlying your model,you may be well served by the <strong>Fractional</strong> Derivative.The solution of the Tautochrone Problem in the next section withthe aid of the Fundamental Theorem, shows thatthe required Convolution Transform modeling and identification isfar from self-evident.14
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