The Grünwald-Letnikov fractional derivative is a fractional derivative defined by a limit of fractional-order backward differences. For lower terminal 
, real order 
,
and 
, the left-sided form is
 |
where 
and 
is a generalized binomial coefficient. For
a positive integer order 
, the sum truncates at 
when 
and gives the ordinary derivative
of order 
in the limit for sufficiently smooth
. If 
and 
is 
times continuously differentiable
on ![[a,b]](/images/equations/Grunwald-LetnikovFractionalDerivative/Inline14.svg)
, this limit agrees with
the Riemann-Liouville fractional
derivative for 
(Podlubny 1999, pp. 52-55 and 75-76).
The Wolfram Language function NFractionalD provides the numerical method Method -> "GrunwaldLetnikov".
