On fractional Duhamel's principle and its applications

TL;DR

This paper develops a fractional generalization of Duhamel's principle, enabling its application to fractional order differential equations, which were previously not covered by the classical principle.

Contribution

It introduces and proves a fractional Duhamel's principle applicable to a broad class of fractional differential-operator equations, extending classical methods.

Findings

Established a fractional Duhamel's principle.

Proved the principle for a wide class of fractional equations.

Extended classical PDE techniques to fractional calculus.

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.