Lectures on Fractional Calculus - CARMA

Technical Details (1)To carry out this calculation, we first need to know∇ 2s r β . It is obvious that each secondderivative reduces the power of r by 2, so∇ 2s r β = K(r, β)r β−2sfor some K(s, β) which depends on β and s,but not r.To evaluate K(s, β) we need Weber’s integral:R ∞0r s J 0 (αr)dr =Γ(1+s2 )2sΓ( 1−s2 )α1+s