This article is cited in 25 papers

On an Inverse Problem for an Abstract Differential Equation of Fractional Order

A. V. Glushak

Belgorod State University

Abstract: In Banach space, we consider the problem of determining the solution and a summand of a differential equation of fractional order from the initial and redundant conditions containing fractional Riemann–Liouville integrals. It is shown that the solvability of the problem under consideration depends on the distribution of zeros of the Mittag–Leffler function.

Keywords: differential equation of fractional order, Riemann–Liouville integral, densely defined linear operator, Mittag–Leffler function, Cesàro mean, Banach space.

UDC: 517.983

Received: 21.01.2008

DOI: 10.4213/mzm4437

 English version: Mathematical Notes, 2010, 87:5, 654–662

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