Górska Katarzyna, Sevilla Francisco J, Chacón-Acosta Guillermo, Sandev Trifce
Institute of Nuclear Physics, Polish Academy of Science, ul. Radzikowskiego 152, PL-31342 Kraków, Poland.
Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, Ciudad de México 01000, Mexico.
Entropy (Basel). 2024 Aug 5;26(8):665. doi: 10.3390/e26080665.
We consider two different time fractional telegrapher's equations under stochastic resetting. Using the integral decomposition method, we found the probability density functions and the mean squared displacements. In the long-time limit, the system approaches non-equilibrium stationary states, while the mean squared displacement saturates due to the resetting mechanism. We also obtain the fractional telegraph process as a subordinated telegraph process by introducing operational time such that the physical time is considered as a Lévy stable process whose characteristic function is the Lévy stable distribution. We also analyzed the survival probability for the first-passage time problem and found the optimal resetting rate for which the corresponding mean first-passage time is minimal.
我们考虑了随机重置下的两种不同的时间分数阶电报方程。使用积分分解方法，我们得到了概率密度函数和均方位移。在长时间极限下，系统趋近于非平衡稳态，而由于重置机制，均方位移会饱和。通过引入运算时间，使得物理时间被视为具有特征函数为 Lévy 稳定分布的 Lévy 稳定过程，我们还得到了作为从属电报过程的分数阶电报过程。我们还分析了首通时间问题的生存概率，并找到了相应的平均首通时间最小的最优重置率。
