Lectures on Fractional Calculus - CARMA

Differentiation of the Logarithm∇ 2s (r β )=i 2s 2 2s Γ(1+β/2)Γ(−β/2)Γ(s−β/2)Γ(1−s+β/2) rβ−2sSuppose we expand this taking β small:r β = e β ln r ' 1+β ln r.Then this will tell us how ∇ 2s operates on a constant and ln r.The only term which causes any problem is1Γ(z) ' z, for |z|