Document Zbl 1206.26007

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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 40 Documents

MSC:

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

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