Well-posedness of time-fractional advection-diffusion-reaction equations

William McLean, Kassem Mustapha, Raed Ali, Omar Knio

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


Abstract We establish the well-posedness of an initial-boundary value problem for a general class of linear time-fractional, advection-diffusion-reaction equations, allowing space- and time-dependent coefficients as well as initial data that may have low regularity. Our analysis relies on novel energy methods in combination with a fractional Gronwall inequality and properties of fractional integrals.
Original languageEnglish (US)
Pages (from-to)918-944
Number of pages27
JournalFractional Calculus and Applied Analysis
Issue number4
StatePublished - Aug 27 2019

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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