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A Marchaud-Hadamard-type fractional derivative and the inversion of Hadamard-type fractional integrals. (Russian) 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.
MSC:
26A33Fractional derivatives and integrals (real functions)
44A15Special transforms (Legendre, Hilbert, etc.)
47G10Integral operators