Regularity theory for time-fractional advection–diffusion–reaction equations

William McLean, Kassem Mustapha, Raed Ali, Omar Knio

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We investigate the behavior of the time derivatives of the solution to a linear time-fractional, advection–diffusion–reaction equation, allowing space- and time-dependent coefficients as well as initial data that may have low regularity. Our focus is on proving estimates that are needed for the error analysis of numerical methods. The nonlocal nature of the fractional derivative creates substantial difficulties compared with the case of a classical parabolic PDE. In our analysis, we rely on novel energy methods in combination with a fractional Gronwall inequality and certain properties of fractional integrals.
Original languageEnglish (US)
Pages (from-to)947-961
Number of pages15
JournalComputers and Mathematics with Applications
Issue number4
StatePublished - Aug 27 2019


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