**author: **R. Herrmann

**abstract:
**

Introducing a set **{α_i}∈R** of fractional exponential powers of focal distances an extension of symmetric Cassini-coordinates on the plane to the asymmetric case is proposed which leads to a new set of fractional generalized Cassini-coordinate systems. Orthogonality and classical limiting cases are derived. An extension to cylindrically symmetric systems in **R³** is investigated. The resulting asymmetric coordinate systems are well suited to solve corresponding two- and three center problems in physics.

**reference: **arXiv:1802.08142