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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.
Contributed by:
Jorge Gamaliel Frade Chávez
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Fractional Derivative
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
An Ordinary Fractional Differential Equation
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/AnOrdinaryFractionalDifferentialEquation/
Contributed by:
Jorge Gamaliel Frade Chávez
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