Fractional advection diffusion asymmetry equation, derivation, solution and application

Wanli Wang, Eli Barkai

Research output: Contribution to journalArticlepeer-review


The non-Markovian continuous-time random walk model, featuring fat-tailed waiting times and narrow distributed displacements with a non-zero mean, is a well studied model for anomalous diffusion. Using an analytical approach, we recently demonstrated how a fractional space advection diffusion asymmetry equation, usually associated with Markovian Lévy flights, describes the spreading of a packet of particles. Since we use Gaussian statistics for jump lengths though fat-tailed distribution of waiting times, the appearance of fractional space derivatives in the kinetic equation demands explanations provided in this manuscript. As applications we analyse the spreading of tracers in two dimensions, breakthrough curves investigated in the field of contamination spreading in hydrology and first passage time statistics. We present a subordination scheme valid for the case when the mean waiting time is finite and the variance diverges, which is related to Lévy statistics for the number of renewals in the process.

Original languageEnglish
Article number035203
JournalJournal of Physics A: Mathematical and Theoretical
Issue number3
StatePublished - 19 Jan 2024


  • anomalous diffusion
  • continuous time random walk
  • fractional advection diffusion asymmetry equation
  • fractional kinetic equations

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • General Physics and Astronomy
  • Statistics and Probability
  • Mathematical Physics
  • Modelling and Simulation


Dive into the research topics of 'Fractional advection diffusion asymmetry equation, derivation, solution and application'. Together they form a unique fingerprint.

Cite this