Fractional Derivative of Sine
Fractional Derivative of Sine
This Demonstration calculates fractional derivatives of the sine function.
The definition of the fractional derivative of a function is
y(x)
-α
d
d
-α
x
1
Γ(a)
x
∫
0
α-1
(x-t)
for and , and
α>0
x>0
α
d
d
α
x
m
d
d
m
x
m-α
d
d
m-α
x
where is any postive integer greater than .
m
α
The fractional derivative of the sine function works out to be
α
d
d
α
x
π
2
"3D View" plots the surface of the function and the red curve in either view is the graph of for constant α.
z=sinx+α
π
2
sinx+α
π
2