A generalized fractional order integral operator is derived that relates the one and two dimensional Green's function for a geometry with parallel plane interfaces. It is found that order of the operator is independent of the geometry while lower limit and operational variable are functions of the geometry. Utilizing the general fractional order operator, it is possible to calculate the fractional solutions for Helmholtz's equation in a geometry with parallel plane interfaces. A generalized expression is proposed for far-zone fractional solution in a geometry with parallel plane interfaces.