On the Leibniz rule and Laplace transform for fractional derivatives
General Mathematics
2020-02-18 v2
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.
Keywords
Cite
@article{arxiv.1901.11138,
title = {On the Leibniz rule and Laplace transform for fractional derivatives},
author = {Yiheng Wei and Da-Yan Liu and Peter W. Tse and Yong Wang},
journal= {arXiv preprint arXiv:1901.11138},
year = {2020}
}