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arXiv · 1805.02309

Precise interpretation of the conformable fractional derivative

Ahmed A. Abdelhakim
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Abstract

Let $\alpha\in\,]0,1[$. We prove that the existence of the conformable fractional derivative $T_{\alpha}f$ of a function $f:[0,\infty[\,\longrightarrow \mathbb{R}$ introduced by Khalil et al. in [R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014) 65-70] is equivalent to classical differentiability. Precisely the fractional $\alpha$-derivative of $f$ is the pointwise product $T_{\alpha}f(x)=x^{1-\alpha}f^{\prime}(x)$, $x>0$. This simplifies the recent results concerning conformable fractional calculus.

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Ahmed A. Abdelhakim. 2018-05-07. Precise interpretation of the conformable fractional derivative. https://arxiv.org/abs/1805.02309

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