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Fractional calculus generalizes ordinary calculus by letting differentiation and integration be of arbitrary order.

The definition of the fractional derivative is

for

and

, and

where

is any postive integer greater than

This Demonstration solves numerically the following ordinary fractional differential equation:

(1)

where

(2)

Here

and

are parameters,

is a dependent variable, and

is an independent variable.

The discretization of equations (1) and (2) are

with

, where

is the gamma function.

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An Ordinary Fractional Differential Equation