An Ordinary Fractional Differential Equation

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

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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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Contributed by: Jorge Gamaliel Frade Chávez (March 2011)
Open content licensed under CC BY-NC-SA


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