An Ordinary Fractional Differential Equation

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.

THINGS TO TRY

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