Geodesic
Laplace transform of fractional order differential equations
Electronic Journal of Differential Equations, Tome 2015 (2015).

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Summary: In this article, we show that Laplace transform can be applied to fractional system. To this end, solutions of linear fractional-order equations are first derived by a direct method, without using Laplace transform. Then the solutions of fractional-order differential equations are estimated by employing Gronwall and Holder inequalities. They are showed be to of exponential order, which are necessary to apply the Laplace transform. Based on the estimates of solutions, the fractional-order and the integer-order derivatives of solutions are all estimated to be exponential order. As a result, the Laplace transform is proved to be valid in fractional equations.
Classification : 26A33, 34A08, 34K37, 44A10
Keywords: fractional-order differential equation, Laplace transform, exponential order 
@article{EJDE_2015__2015__a76,
     author = {Liang, Song and Wu, Ranchao and Chen, Liping},
     title = {Laplace transform of fractional order differential equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a76/}
}
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Liang, Song; Wu, Ranchao; Chen, Liping. Laplace transform of fractional order differential equations. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a76/