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This paper studies random fields on the unit sphere. Traditionally, isotropicGaussian random fields are considered as the underlying statistical model ofthe cosmic microwave background (CMB) data. This paper discusses thegeneralized multifractional Brownian motion and its pointwise H\"older exponenton the sphere. The multifractional approach is used to investigate the CMB datafrom the Planck mission. These data consist of CMB radiation measurements atnarrow angles of the sky sphere. The obtained results suggest that theestimated H\"older exponents for different CMB regions do change from locationto location. Therefore, CMB data are multifractional. Then the developedmethodology is used to suggest two approaches for detecting regions withanomalies in cleaned CMB maps.

On Multifractionality of Spherical Random Fields with Cosmological Applications