Geodesic
A Fractional Analog of the Duhamel Principle
Fractional calculus and applied analysis, Tome 9 (2006) no. 1, pp. 57-70.

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The well known Duhamel principle allows to reduce the Cauchy problem for linear inhomogeneous partial differential equations to the Cauchy problem for corresponding homogeneous equations. In the paper one of the possible generalizations of the classical Duhamel principle to the time-fractional pseudo-differential equations is established.
Keywords: Duhamel's Principle, Pseudo-Differential Equations, Cauchy Problem, Inhomogeneous Equation, Time-Fractional Equation, 35CXX, 26A33, 35S10 
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Umarov, Sabir; Saydamatov, Erkin. A Fractional Analog of the Duhamel Principle. Fractional calculus and applied analysis, Tome 9 (2006) no. 1, pp. 57-70. http://geodesic.mathdoc.fr/item/FCAA_2006_9_1_a4/