Zeitschrift für Analysis und ihre Anwendungen
Full-Text PDF (315 KB) | Metadata | Table of Contents | ZAA summary
Published online: 2016-10-05
Which Functions are Fractionally Differentiable?Gennadi Vainikko (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 differentiation 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