The Debye theory of dielectric relaxation of an assembly of polar molecules is reformulated using a fractional noninertial Fokker-Planck equation for the purpose of extending that theory to explain anomalous dielectric relaxation. The fractional Fourier-Planck equation in question is a generalization of the Smoluchowski equation for the dynamics of Brownian particles in configuration space to include anomalous relaxation. It is shown that this model can reproduce nonexponential Cole-Cole-type anomalous dielectric relaxation behavior and that it reduces to the classical Debye model of rotational diffusion when the anomalous exponent is unity.