时间重参数化，而非分数微积分：对符合导数的重新评估
Time Reparametrization, Not Fractional Calculus: A Reassessment of the Conformable Derivative
AI总结：
本文重新评估了符合导数，指出其并非分数微积分，而是用于幂律时间缩放的计算工具，揭示经典微分在非线性时间重参数化下的等价性，并通过理论和数值分析说明经典和分数导数在建模记忆依赖现象中的优势。
摘要：
符合导数已被众多出版物推广为一种新的分数导数算子。本文对这一主张进行了批判性重新评估。我们证明符合导数不是一个分数算子，而是一个有用的计算工具，用于具有幂律时间缩放的系统，等同于在非线性时间重参数化下的经典微分。文献中提出的几个结果作为新的分数贡献可以重新解释在经典框架内。我们展示了使用符合导数的问题可以转换为经典形式，通过变量替换。解是经典求解后转换回来，这种重新解释突显了没有真正非局部分数效应的缺失。我们提供了理论分析，比较符合、经典和真正分数（Caputo）模型的数值模拟，并讨论了这一误解持续的原因。我们的结果表明，经典导数以及已建立的分数导数提供了一个更忠实的框架来建模记忆依赖现象。
英文摘要：
The conformable derivative has been promoted in numerous publications as a new fractional derivative operator. This article provides a critical reassessment of this claim. We demonstrate that the conformable derivative is not a fractional operator but a useful computational tool for systems with power-law time scaling, equivalent to classical differentiation under a nonlinear time reparametrization. Several results presented in the literature as novel fractional contributions can be reinterpreted within a classical framework. We show that problems formulated using the conformable derivative can be transformed into classical formulations via a change of variable. The solution is derived classically and then transformed back, this reformulation highlights the absence of genuinely nonlocal fractional effects. We provide a theoretical analysis, numerical simulations comparing conformable, classical, and truly fractional (Caputo) models, and discuss the reasons why this misconception persists. Our results suggest that classical derivatives, as well as established fractional derivatives, offer a more faithful framework for modeling memory-dependent phenomena.
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