Fractional diffusions with time-varying coefficients

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 $L^{\alpha }$ 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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Cited by in corpus (6)

• The Wright functions of the second kind in Mathematical Physics
• Stochastic solutions of generalized time-fractional evolution equations
• Multifractality of jump diffusion processes
• Subdiffusion with Time-Dependent Coefficients: Improved Regularity and Second-Order Time Stepping
• Recovery of a Space-Time Dependent Diffusion Coefficient in Subdiffusion: Stability, Approximation and Error Analysis
• Fractional Brownian motions ruled by nonlinear equations