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Memory-dependent derivative versus fractional derivative (I): Difference in temporal modeling

机译:内存依赖衍生物与分数衍生物(i):时间建模差异

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摘要

Since the memory-dependent derivative (MDD) was developed in 2011, it has become a new branch of Fractional Calculus which is still in the ascendant nowadays. How to understand MDD and fractional derivative (FD)? What are the advantages and disadvantages for them? How do they behave in Modeling? These questions guide going deep into the illustration of memory effect. Though the FD is defined on an interval, it mainly reflects the local change. Relative to the FD, the physical meaning of MDD is much clearer. The time-delay reflects the duration of memory effect, and the kernel function reflects the dependent weight. The results show that the MDD is more suitable for temporal modeling. In addition, a numerical algorithm for MDD is also developed here. (C) 2020 Elsevier B.V. All rights reserved.
机译:自2011年提出记忆依赖导数(MDD)以来,它已成为分数阶微积分的一个新分支,目前仍在方兴未艾。如何理解MDD和分数阶导数(FD)?它们的优点和缺点是什么?他们在建模时表现如何?这些问题引导我们深入研究记忆效应。虽然FD是按区间定义的,但它主要反映局部变化。相对于FD,MDD的物理意义更为明确。时滞反映了记忆效应的持续时间,核函数反映了相关权重。结果表明,MDD更适合于时态建模。此外,本文还提出了一种求解MDD的数值算法。(C) 2020爱思唯尔B.V.版权所有。

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