Fractional Telegrapher's Equation under Resetting: Non-Equilibrium Stationary States and First-Passage Times

• Published in: Entropy (Basel, Switzerland) Vol. 26; no. 8; p. 665
• Main Authors: Górska, Katarzyna, Sevilla, Francisco J, Chacón-Acosta, Guillermo, Sandev, Trifce
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 05.08.2024; MDPI
• Subjects: Boundary conditions; Characteristic functions; Decomposition; Distribution (Probability theory); first-passage time; Fourier transforms; Laplace transforms; Normal distribution; Probability density functions; Probability distribution functions; Propagation; stochastic resetting; telegrapher’s equation; United Kingdom; stochastic resetting; first-passage time; telegrapher’s equation
• ISSN: 1099-4300; 1099-4300
• 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.