be the Riemann-Liouville fractional derivative of
. Consider the linear differential operator
with constant coefficients given by
. The authors analyze fractional differential equations (FDE) of the form
is the derivative of a Lévy process in the distribution sense. The Green function solution of the FDE is of the form
is the Green function with the Laplace transform
. Some exact results on the Green functions, covariance functions, spectra, and higher-order spectra of particular forms of FDE are obtained. The FDE can be applied to stochastic volatility of asset prices and to macroeconomics.