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Zeitschrift für Analysis und ihre Anwendungen

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Volume 35, Issue 4, 2016, pp. 465–487
DOI: 10.4171/ZAA/1574

Published online: 2016-10-05

Which Functions are Fractionally Differentiable?

Gennadi Vainikko[1]

(1) Tartu University, Estonia

We examine the existence of fractional derivatives of a function in terms of the pointwise convergence or equiconvergence of certain improper integrals containing this function. The fractional di fferentiation operator is treated as the inverse to the Riemann-Liouville integral operator. Technically, we give a description of the range of the Riemann-Liouville operator. The results are reformulated also for Riemann-Liouville and Caputo fractional derivatives.

Keywords: Inversion of Riemann-Liouville operator, Riemann-Liouville fractional derivative, Caputo fractional derivative, description of fractionally differentiable functions

Vainikko Gennadi: Which Functions are Fractionally Differentiable?. Z. Anal. Anwend. 35 (2016), 465-487. doi: 10.4171/ZAA/1574