This article is cited in 6 papers

On the Properties of a Cauchy-Type Problem for an Abstract Differential Equation with Fractional Derivatives

A. V. Glushak

Belgorod State University

Abstract: We study the relationship between the solutions of abstract differential equations with fractional derivatives and their stability with respect to the perturbation by a bounded operator. Besides, we obtain representations for the solution of an inhomogeneous equation and for an equation containing a fractional power of the generator of a cosine operator function.

Keywords: differential equation with fractional derivatives, Cauchy-type problem, Riemann–Liouville fractional derivative, fractional integral, Mittag-Leffler function.

UDC: 517.983

Received: 09.02.2005
Revised: 10.04.2007

DOI: 10.4213/mzm4081

 English version: Mathematical Notes, 2007, 82:5, 596–607

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