Abstract
The regularity of solutions of the equation (u - u 0)) (t,x) + c(t,x)u x(t,x) = f(t,x), t, x > 0, where denotes the fractional derivative, is studied. It is shown that if c and f are Hölder continuous in either t or x and c is strictly positive, then both u x and (u — u 0) are Hölder continuous as well (in either t or x).
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Clément, P., Gripenberg, G., Londen, SO. (1999). Hölder Regularity for a Linear Fractional Evolution Equation. In: Escher, J., Simonett, G. (eds) Topics in Nonlinear Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 35. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8765-6_5
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DOI: https://doi.org/10.1007/978-3-0348-8765-6_5
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9764-8
Online ISBN: 978-3-0348-8765-6
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