The Grünwald–Letnikov definition of the fractional derivative of order
is given by the expression
represents the gamma function and
the increment. We verify that
can be viewed as the expected value of the discrete random variable that for
takes the value
The Grünwald–Letnikov definition gets the slope of a triangle with upper corners
. The factor
in the denominator expression means that, for large values of
, we have a slow variation, while for small values of
we have a fast variation.
The implementation of the Grünwald–Letnikov definition of the fractional derivative corresponds to an
-term truncated series given by
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