Two dimensional Green's function for non-integer dimensional dielectric half space geometry

Two dimensional Green's function for non-integer dimensional dielectric half space geometry has been derived. It has been assumed that both half spaces are of non-integer dimension. Radiated fields are written as unknown spectrum of plane waves for non-integer dimensional space. Unknown spectrum functions are derived using the boundary conditions. Special cases with one of the two or both half spaces taken as integer dimensional have also been addressed.