27 citations · 38 across the 6 of their papers we have counts for
4 papers · 1 filter
Space-time coupled evolution equations and their stochastic solutions
John Herman, Ifan Johnston, Lorenzo Toniazzi
We consider a class of space-time coupled evolution equations (CEEs), obtained by a subordination of the heat operator. Our CEEs reformulate and extend known governing equations of…
Stochastic representation of solution to nonlocal-in-time diffusion
Qiang Du, Lorenzo Toniazzi, Zhi Zhou
The aim of this paper is to give a stochastic representation for the solution to a natural extension of the Caputo-type evolution equation. The nonlocal-in-time operator is defined…
Stochastic solutions for space-time fractional evolution equations on bounded domain
Lorenzo Toniazzi
Space-time fractional evolution equations are a powerful tool to model diffusion displaying space-time heterogeneity. We prove existence, uniqueness and stochastic representation o…
Generalised Fractional Evolution Equations of Caputo Type
M. E. Hernández-Hernández, V. N. Kolokoltsov, L. Toniazzi
This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obt…