Which Functions are Fractionally Differentiable?

  • Gennadi Vainikko

    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.

Cite this article

Gennadi Vainikko, Which Functions are Fractionally Differentiable?. Z. Anal. Anwend. 35 (2016), no. 4, pp. 465–487

DOI 10.4171/ZAA/1574