An Ordinary Fractional Differential Equation
Fractional calculus generalizes ordinary calculus by letting differentiation and integration be of arbitrary order.[more]
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:
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.[less]