fractional calculus

The idea of calculus in fractional order is nearly as old as its integer counterpart. In a letter dated September 30th 1650, l’Hôpital posed the question of the meaning of ${\displaystyle \frac{d^{\alpha }f}{d{x}^{\alpha }}}$ if $\alpha ={\displaystyle \frac{1}{2}}$ to Leibniz. There are different approaches to define calculus of fractional order. The following approaches are the most common and we can prove that they are equivalent

(1) Riemann-Liouville approach of fractional integration

(2) Grunwald-Letnikov approach of fractional differentiation

Title	fractional calculus
Canonical name	FractionalCalculus
Date of creation	2013-03-22 16:18:27
Last modified on	2013-03-22 16:18:27
Owner	bchui (10427)
Last modified by	bchui (10427)
Numerical id	14
Author	bchui (10427)
Entry type	Definition
Classification	msc 28B20
Synonym	fractional calculus
Defines	fractional calculus