Fractional Calculus - Gauge-institute.org

Gauge Institute Journal, Volume 5, No 1, February 2009H. Vic Dannon12 1≡212df( dx ( − a))as the convolution of the function f () x , with the Kernel functionDfx −32Γ− ( )12, over the interval [ ax , ]u31= x3 x− 2−We use the notations( )2∫ x −u f( u) du ≡ ∗ f( x).Γ− ( ) Γ− ( )1 12 u=a211 df21−32≡ ≡21 1 ∫ −2Df ( x u) fudu ( )Γ− ( )( dx ( − a))2u=xu=a7