Three-dimensional beampatterns can be flexibly and efficiently designed in the spherical harmonics domain. This has a number of useful applications such as beamforming the signals received by spherical microphone arrays, or controlling radiating sound beams produced by compact spherical loudspeaker arrays. However, with the existing design methods, the beampattern orders are restricted to integer numbers. In this paper, we present an approach to the design of axis-symmetric spherical beampatterns with fractional orders. This is typically useful in audio applications where smooth user control is desirable. First, we derive an analytical expression of the fractionalorder beamforming weights, so that the beampattern matches a design objective such as a target directivity index. Then, we present an example of spherical hyper-cardioid pattern (for which the analytical solution is particularly concise) which effectively achieves continuously adjustable directivity index. Our results are in line with a similar study previously published by Huang et al. (2018), yet our approach is both simpler and more generic. As another novel contribution, we extend the method to fractional-order cardioid, super-cardioid, and max-rE beampatterns.