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