On the Leibniz rule and Laplace transform for fractional derivatives

Yiheng Wei; Da-Yan Liu; Peter W. Tse; Yong Wang

doi:10.1080/10652469.2019.1694923

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arXiv · 1901.11138

On the Leibniz rule and Laplace transform for fractional derivatives

Yiheng Wei·Da-Yan Liu·Peter W. Tse·Yong Wang

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Abstract

Taylor series is a useful mathematical tool when describing and constructing a function. With the series representation, some properties of fractional calculus can be revealed clearly. This paper investigates two typical applications: Lebiniz rule and Laplace transform. It is analytically shown that the commonly used Leibniz rule cannot be applied for Caputo derivative. Similarly, the well-known Laplace transform of Riemann-Liouville derivative is doubtful for n-th continuously differentiable function. By the aid of this series representation, the exact formula of Caputo Leibniz rule and the explanation of Riemann-Liouville Laplace transform are presented. Finally, three illustrative examples are revisited to confirm the obtained results.

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BibTeX RIS

Yiheng Wei, Da-Yan Liu, Peter W. Tse, Yong Wang. 2020-02-16. On the Leibniz rule and Laplace transform for fractional derivatives. https://doi.org/10.1080/10652469.2019.1694923

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