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

William McLean, Kassem Mustapha, Raed Ali, Omar Knio

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

Abstract

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
Volume22
Issue number4
DOIs
StatePublished - Aug 27 2019

Bibliographical note

KAUST Repository Item: Exported on 2021-12-15
Acknowledged KAUST grant number(s): KAUST005
Acknowledgements: The authors thank the University of New South Wales (Faculty Research Grant “Efficient numerical simulation of anomalous transport phenomena”), the King Fahd University of Petroleum and Minerals (project No. KAUST005) and the King Abdullah University of Science and Technology.

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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