# 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 $\displaystyle{\frac{d^{\alpha}f}{dx^{\alpha}}}$ if $\displaystyle{\alpha=\frac{1}{2}}$ 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 FractionalCalculus 2013-03-22 16:18:27 2013-03-22 16:18:27 bchui (10427) bchui (10427) 14 bchui (10427) Definition msc 28B20 fractional calculus fractional calculus