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arXiv · 1912.04422

On the mistake in defining fractional derivative using a non-singular kernel

Edmundo Capelas de Oliveira·Stefania Jarosz·Jayme Vaz Jr
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Abstract

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.

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Edmundo Capelas de Oliveira, Stefania Jarosz, Jayme Vaz Jr. 2019-12-09. On the mistake in defining fractional derivative using a non-singular kernel. https://arxiv.org/abs/1912.04422

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