I remember rediscovering fractional derivatives in college after learning about the Laplace transform derivative formula. I even called them fractional derivatives; and have a maple notebook somewhere in which I identified some fractional derivatives for various smooth functions. An interesting fact is that:
sin^(a)(x) = sin(x+a*pi/2)
(perhaps with some normalizing factor in front).
thus d/dx sin(x) = cos(x), etc.
I found the symmetry of this to be really beautiful.
I was very proud of my accomplishment until I googled the term and realized someone had beat me to it by ~50-100 years :)
sin^(a)(x) = sin(x+a*pi/2)
(perhaps with some normalizing factor in front).
thus d/dx sin(x) = cos(x), etc.
I found the symmetry of this to be really beautiful.
I was very proud of my accomplishment until I googled the term and realized someone had beat me to it by ~50-100 years :)