Fractional diffusions with time-varying coefficients (original) (raw)
Abstract
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 α into Erdélyi-Kober fractional integrals. We study also probabilistic properties of the r.v.'s 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 r.v.'s.
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