On the mistake in defining fractional derivative using a non-singular kernel
| Autor: | de Oliveira, Edmundo Capelas, Jarosz, Stefania, Vaz Jr, Jayme |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Definitions of fractional derivative of order $\alpha$ ($0 < \alpha \leq 1$) using non-singular kernels have been recently proposed. In this note we show that these definitions cannot be useful in modelling problems with a initial value condition (like, for example, the fractional diffusion equation) because the solutions obtained for these equations do not satisfy the initial condition (except for the integer case $\alpha = 1$). In order to satisfy an arbitrary initial condition the definitions of fractional derivative must necessarily involve a singular kernel. Comment: References and extra comments added. 9 pages |
| Databáze: | arXiv |
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