arXiv subjects

M. E. Hernández-Hernández

Publications and source records attributed to M. E. Hernández-Hernández.

2 recordsLinked to original sources

arXiv2017

Generalised Fractional Evolution Equations of Caputo Type

This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations for the solutions. These results encompass known linear and non-linear equations from classical fractional partial differential equations such as the time-space-fractional diffusion equation, as well as their far reaching extensions. \\ Meaning is given to a probabilistic generalisation of Mittag-Leffler functions.

math.AP↗

arXiv2015

On the probabilistic approach to the solution of generalized fractional differential equations of Caputo and Riemann-Liouville type

This paper provides a probabilistic approach to solve linear equations involving Caputo and Riemann-Liouville type derivatives. Using the probabilistic interpretation of these operators as the generators of interrupted Feller processes, we obtain well-posedness results and explicit solutions (in terms of the transition densities of the underlying stochastic processes). The problems studied here include fractional linear differential equations, well analyzed in the literature, as well as their far reaching extensions.

math.PR↗