28 jan 2025 -- 16:30   [open in google calendar]

Abstract.

Non-Markovian continuous-time random walk (CTRW) on homogeneous space in the uncoupled formulation are considered. Non-Markovianity is set by a power-lawed waiting-time density providing an infinite-mean waiting-time. The evolution equations for the survival probability and for the first-passage time density are derived. The evolution equation for the survival probability results in a time-fractional equation in the Caputo sense while that for the first-passage time density results in the same equation but in the Riemann--Liouville sense. This difference implies related issues about the initial conditions. The relation between the solutions in the Markovian and non-Markovian settings for both equations is also established.