A generalization of Duhamel's principle for differential equations of fractional order

A generalization of Duhamel's classical principle to differential equations of fractional order is discussed. It is found that Duhamel's principle reduces the Cauchy problem for inhomogeneous linear partial differential equations, to the Cauchy problem for the corresponding homogeneous equation. Result shows that the inhomogeneous problems, can be solved by the use and estimation of Green's functions or application of a combination of some integral transformations and Duhamel's classification principle.