Spectral entropy in a fractional order model of anomalous diffusion

Fractional order dynamic models of complex systems provide improved fits to experimental data with a reduced mean-squared error. The success of this approach, however, is dependent on the order of the derivatives included in the model. Fractional order models, for example, work better in describing the electrical and mechanical properties of multi-scale, heterogeneous materials than do integer order models. In order to estimate a measure of the expected improvement provided by fractional order models, we calculate the spectral entropy for anomalous diffusion as governed by the generalized diffusion equation in space and time. This fractional order representation of diffusion gives a minimum spectral entropy for Gaussian diffusion and predicts an increasing spectral entropy for non-Gaussian, or fractional, diffusion.