Kilbas, A. A.; Tityura, A. A. A Marchaud-Hadamard-type fractional derivative and the inversion of Hadamard-type fractional integrals. (Russian. English summary) Zbl 1206.26007 Dokl. Nats. Akad. Nauk Belarusi 50, No. 4, 5-10 (2006). Summary: Hadamard-type fractional integrals and derivatives on the half-axis are investigated in weighted spaces of \(p\)-summable functions. Integral representations for Marchaud-Hadamard-type fractional derivatives are established. Conditions for inversion of the Hadamard-type fractional integrals are given. Relationships between the ordinary and truncated Marchaud-Hadamard-type fractional derivatives are proved. Cited in 38 Documents MSC: 26A33 Fractional derivatives and integrals 44A15 Special integral transforms (Legendre, Hilbert, etc.) 47G10 Integral operators PDF BibTeX XML Cite \textit{A. A. Kilbas} and \textit{A. A. Tityura}, Dokl. Nats. Akad. Nauk Belarusi 50, No. 4, 5--10 (2006; Zbl 1206.26007) OpenURL