Cauchy problem for a fractional anisotropic parabolic equation in anisotropic Hölder spaces

<p style='text-indent:20px;'>We consider a Cauchy problem for fractional anisotropic parabolic equation in Hölder spaces. The generalizes the heat to case of power Laplace operator and this can be different with respect groups space variables. time derivative either Caputo - Jrbashyan or usual derivative. Under some necessary conditions on order we show that whole is an isomorphism appropriate another prove unique solvability same spaces.</p>