Lectures on Fractional Calculus - CARMA

The Green’s function in 2DWe start with(2π) 2 δ 2 (k x ,k y )= R ∞−∞ dxdyei(k xx+k y y)and∇ R 2 ∞−∞ dxdyei(k xx+k y y) =− R ∞−∞ dxdy(k2 x + k 2 y)e i(k xx+k y y)HenceG(x, y) = 14π 2 R ∞−∞R ∞−∞e i(k xx+ky y)(k 2 x +k2 y )Theintegralisdoneinpolarcoordinates:k x = r cos(θ), k y = r sin(θ).