# 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