First passage time for $g$--subdiffusion process of vanishing particles

TL;DR

This paper derives the first-passage time distribution for a generalized subdiffusion process where molecules can vanish, incorporating functions that modify timescales and their mutual influence, extending classical models.

Contribution

It introduces a novel framework for first-passage time analysis in g-subdiffusion processes with molecule disappearance, accounting for the relationship between subdiffusion and survival functions.

Findings

Derived the first-passage time distribution for g-subdiffusion with vanishing particles.

Showed how the functions g1 and g2 influence the process and can be related.

Provided an example with highly related subdiffusion and survival processes.

Abstract

Subdiffusion equation and molecule survival equation, both with Caputo fractional time derivatives with respect to another functions $g_1$ and $g_2$, respectively, are used to describe diffusion of a molecule that can disappear at any time with a constant probability. The process can be interpreted as ``ordinary'' subdiffusion and ``ordinary'' molecule survival process in which timescales are changed by the functions $g_1$ and $g_2$. We derive the first-passage time distribution for the process. The mutual influence of subdiffusion and molecule vanishing processes can be included in the model when the functions $g_1$ and $g_2$ are related to each other. As an example, we consider the processes in which subdiffusion and molecule survival are highly related, which corresponds to the case of $g_1\equiv g_2$.