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

Area of Science:

• Physics
• Chemistry
• Mathematical Modeling

Background:

• Subdiffusion describes anomalous molecular movement where particles move slower than predicted by Brownian motion.
• Molecule survival equations model the probability of a molecule persisting over time, considering decay or disappearance.
• Fractional calculus offers advanced tools to describe complex, non-local temporal dynamics in physical and chemical processes.

Purpose of the Study:

• To develop a unified mathematical framework for subdiffusion with time-dependent vanishing probabilities.
• To derive the first-passage time distribution for this combined process.
• To analyze the interplay between subdiffusion dynamics and molecule disappearance rates.

Main Methods:

• Utilizing Caputo fractional time derivatives with respect to general time-scaling functions g1 and g2.
• Deriving the first-passage time probability distribution function.
• Analyzing the specific case where g1 is identical to g2, indicating a strong coupling between subdiffusion and survival.

Main Results:

• The study successfully derives the first-passage time distribution for subdiffusion with time-dependent molecule vanishing.
• It demonstrates how the functions g1 and g2 modify the characteristic timescales of both subdiffusion and survival.
• A significant finding is the ability to model the mutual influence of these processes when g1 and g2 are related.

Conclusions:

• The developed model provides a flexible approach to studying complex molecular dynamics involving anomalous diffusion and decay.
• The first-passage time distribution is a key metric for understanding the temporal behavior of such systems.
• The framework highlights the importance of considering coupled dynamics for accurate predictions in related scientific fields.