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Licensed Unlicensed Requires Authentication Published by De Gruyter October 23, 2019

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

William McLean, Kassem Mustapha, Raed Ali and Omar Knio


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.


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.


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Received: 2018-11-15
Published Online: 2019-10-23
Published in Print: 2019-08-27

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