Boundary condition defined in Fourier space

[Sadokat]

Dear All,

I am working with Dedalus v3, my vector field u is defined using a mixed basis RealFourier in x and y, and Chebyshev in z. Mathematically I derived the Robin type boundary condition in Forier space, something like: 

∂z û (z) + k_⊥ û (z) = 0, on z=Lz.

where k_⊥ = sqrt(kx² + ky²). 

Are there any approaches in Dedalus for operators related to fractional Laplacians (−Δ_⊥)^{−1/2}? 

 I would appreciate some guidance on how to properly formulate this kind of  boundary condition. 

with best regards,

Sadokat