Vipul: Created page with "==Definition== The '''Grünwald–Letnikov derivative''' is an attempt to define a generalization for the iterated derivative to a non-integer number of iterations. For a..."

2014-04-24T01:51:57Z

Created page with "==Definition== The '''Grünwald–Letnikov derivative''' is an attempt to define a generalization for the iterated derivative to a non-integer number of iterations. For a..."

New page

==Definition==

The '''Grünwald–Letnikov derivative''' is an attempt to define a generalization for the [[iterated derivative]] to a non-integer number of iterations. For a real number <math>q</math>, a function <math>f</math>, and a real number <math>h</math>, define:

<math>\Delta^q_hf(x) = \sum_{0 \le m < \infty}(-1)^m {q \choose m}f(x+(q-m)h)</math>

Then, we define:

<math>\mathbb{D}^q f(x) = \lim_{h \to 0}\frac{\Delta^q_h f(x)}{h^q}</math>

==See also==

* [[Riemann-Louiville fractional integral]] (this also allows us to compute the Riemann-Liouville fractional ''derivative'')

Grünwald–Letnikov derivative - Revision history

Vipul: Created page with "==Definition== The '''Grünwald–Letnikov derivative''' is an attempt to define a generalization for the iterated derivative to a non-integer number of iterations. For a..."