11562
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
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
THINGS TO TRY
Gamepad Controls
SNAPSHOTS
RELATED LINKS
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
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Fractional Derivative of Sine
Jorge Gamaliel Frade Chávez
Fractional Derivative of a Power
Jorge Gamaliel Frade Chávez
Differential of a Function
Izidor Hafner
Total Differential of the First Order
Izidor Hafner
Geometric Difference between a Finite Difference and a Differential
Anping Zeng (Sichuan Chemical Technical College)
Automatic Differentiation
Roger B. Kirchner
Cyclic Functions under Differentiation
William Perry
Boole Differential Equation with Continued Fractions
Andreas Lauschke
Riccati Differential Equation with Continued Fractions
Andreas Lauschke
Difference Equation versus Differential Equation
Luis R. Izquierdo and Segismundo S. Izquierdo
Related Topics
Calculus
Derivatives
Differential Equations
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+