Electron. J. Diff. Equ., Vol. 2015 (2015), No. 139, pp. 1-15.

Laplace transform of fractional order differential equations

Song Liang, Ranchao Wu, Liping Chen

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.

Submitted October 10, 2014. Published May 20, 2015.
Math Subject Classifications: 26A33, 34A08, 34K37, 44A10.
Key Words: Fractional-order differential equation; Laplace transform; exponential order.

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Song Liang
School of Mathematics, Anhui University
Hefei 230601, China
email: songliangeq@163.com
Ranchao Wu
School of Mathematics, Anhui University
Hefei 230601, China
email: rcwu@ahu.edu.cn
Liping Chen
School of Electrical Engineering and Automation
Hefei University of Technology
Hefei 230009, China
email: lip_chenhut@126.com

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