分数阶Duhamel原理及其应用
On fractional Duhamel's principle and its applications
摘要：
经典的杜哈梅尔原理，由Jean-Marie-Constant Duhamel在近200年前建立，将非齐次偏微分方程的柯西问题转化为相应齐次方程的柯西问题。Duhamel原理不适用于分数阶微分方程。在本文中，我们制定和证明分数推广这一著名的原则直接适用于广泛的一类分数阶微分算子方程。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
