On fractional Duhamel's principle and its applications

2010/04/13 by Sabir Umarov, Umarov, Sabir
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1004.2098

20 pages

arxiv created 2010/04/13 · arxiv updated 2010/04/14

Abstract

The classical Duhamel principle, established nearly 200 years ago by Jean-Marie-Constant Duhamel, reduces the Cauchy problem for an inhomogeneous partial differential equation to the Cauchy problem for the corresponding homogeneous equation. Duhamel's principle is not applicable in the case of fractional order differential equations. In this paper we formulate and prove fractional generalizations of this famous principle directly applicable to a wide class of fractional order differential-operator equations.

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