Entropy Production Rate of a One-Dimensional Alpha-Fractional Diffusion Process

In this paper, the one-dimensional α-fractional diffusion equation is revisited. This equation is a particular case of the timeand space-fractional diffusion equation with the quotient of the orders of the timeand space-fractional derivatives equal to one-half. First, some integral representations of its fundamental solution including the Mellin-Barnes integral representation are derived. Then a series representation and asymptotics of the fundamental solution are discussed. The fundamental solution is interpreted as a probability density function and its entropy in the Shannon sense is calculated. The entropy production rate of the stochastic process governed by the α-fractional diffusion equation is shown to be equal to one of the conventional diffusion equation.