A Marchaud-Hadamard-type fractional derivative and the inversion of Hadamard-type fractional integrals. (Russian. English summary) Zbl 1206.26007

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.


26A33 Fractional derivatives and integrals
44A15 Special integral transforms (Legendre, Hilbert, etc.)
47G10 Integral operators