Fractional Derivative

Author

Eric W. Weisstein
April 14, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Calculus/FractionalDerivative.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/FractionalDerivative.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Code

FractionalD[nu_,f_,t_,opts___]:=Integrate[(t-x)^(-nu-1)(f/.t->x),{x,0,t},opts]/Gamma[-nu]

FractionalD[mu_?Positive,f_,t_,opts___]:=Module[{m=Ceiling[mu]},
D[FractionalD[-(m-mu),f,t,opts],{t,m}]
]

Constant Function

Limit[(((t^(-μ+λ)) Gamma[1+λ])/(Gamma[λ-μ+1])),λ->0]

Semiderivative

Power

(((t^(-μ+λ)) Gamma[1+λ])/(Gamma[λ-μ+1]))/. μ->1/2

Constant Function

Limit[%,λ->0]