Higher order Grünwald approximations of fractional derivatives and fractional powers of operators

Baeumer, Boris; Kovács, Mihály; Sankaranarayanan, Harish

doi:10.1090/S0002-9947-2014-05887-X

Higher order Grünwald approximations of fractional derivatives and fractional powers of operators
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by Boris Baeumer, Mihály Kovács and Harish Sankaranarayanan PDF

Trans. Amer. Math. Soc. 367 (2015), 813-834 Request permission

Abstract:

We give stability and consistency results for higher order Grünwald-type formulae used in the approximation of solutions to fractional-in-space partial differential equations. We use a new Carlson-type inequality for periodic Fourier multipliers to gain regularity and stability results. We then generalise the theory to the case where the first derivative operator is replaced by the generator of a bounded group on an arbitrary Banach space.

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