Fractional diffusions with time-varying coefficients

This paper is concerned with the fractionalized diffusion equations governing the law of the fractional Brownian motion B-H(t). We obtain solutions of these equations which are probability laws extending that of B-H(t). Our analysis is based on McBride fractional operators generalizing the hyper-Bessel operators L and converting their fractional power L-alpha into Erdelyi-Kober fractional integrals. We study also probabilistic properties of the random variables whose distributions satisfy space-time fractional equations involving Caputo and Riesz fractional derivatives. Some results emerging from the analysis of fractional equations with time-varying coefficients have the form of distributions of time-changed random variables. (C) 2015 AIP Publishing LLC.