A novel generalized fractional-order memristor model with fully explicit memory description,International Journal of Circuit Theory and Applications

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A novel generalized fractional-order memristor model with fully explicit memory description
International Journal of Circuit Theory and Applications ( IF 1.8 ) Pub Date : 2022-08-22 , DOI: 10.1002/cta.3410
Rawid Banchuin ₁

Affiliation

In this work, a novel generalized mathematical model of fractional-order memristor with fully explicit memory description has been proposed. For obtaining such full explicit memory description, the Atangana-Baleanu fractional derivative in Liouville-Caputo sense, which employs a nonsingular kernel, has been adopted as the mathematical basis. The proposed model has been derived without regarding to any specific conventional memristor. A comparison with the singular kernel fractional derivative-based model has been made. The behavioral analysis of the fractional-order memristor based on the proposed model has been performed, where both DC and AC stimuli have been considered. In addition, its application to the practical fractional-order memristor-based circuit and its extension to the fractional-order memreactance have also been shown. Unlike the singular kernel fractional derivative-based model, a fully explicit memory description can be obtained by ours. Many other interesting results that are contradict to the previous singular kernel fractional derivative-based ones, e.g., the fractional-order memristor that can be locally active, have been demonstrated. The abovementioned extension can be conveniently performed. In summary, this is the first time that a nonsingular kernel fractional derivative has been applied to the fractional-order memristor modeling and the resulting model with a fully explicit memory description has been proposed. The proposed model is also highly generic, applicable to the practical circuit, and extendable to the fractional-order memreactance.

中文翻译：

一种具有完全显式记忆描述的新型广义分数阶忆阻器模型

在这项工作中，提出了一种具有完全显式存储器描述的分数阶忆阻器的新型广义数学模型。为了获得这种完整的显式记忆描述，Liouville-Caputo 意义上的 Atangana-Baleanu 分数阶导数采用非奇异核作为数学基础。所提出的模型是在不考虑任何特定传统忆阻器的情况下推导出来的。与基于奇异核分数阶导数的模型进行了比较。基于所提出的模型对分数阶忆阻器进行了行为分析，其中考虑了直流和交流刺激。此外，还展示了它在实际分数阶忆阻器电路中的应用及其对分数阶忆阻器的扩展。与基于奇异核分数阶导数的模型不同，我们可以获得完全显式的记忆描述。许多其他有趣的结果与以前基于奇异核分数阶导数的结果相矛盾，例如，可以局部激活的分数阶忆阻器，已经被证明。可以方便地进行上述扩展。总之，这是第一次将非奇异核分数阶导数应用于分数阶忆阻器建模，并提出了具有完全显式记忆描述的结果模型。所提出的模型还具有高度通用性，适用于实际电路，并且可扩展到分数阶磁电抗。许多其他有趣的结果与以前基于奇异核分数阶导数的结果相矛盾，例如，可以局部激活的分数阶忆阻器，已经被证明。可以方便地进行上述扩展。总之，这是第一次将非奇异核分数阶导数应用于分数阶忆阻器建模，并提出了具有完全显式记忆描述的结果模型。所提出的模型还具有高度通用性，适用于实际电路，并且可扩展到分数阶磁电抗。许多其他有趣的结果与以前基于奇异核分数阶导数的结果相矛盾，例如，可以局部激活的分数阶忆阻器，已经被证明。可以方便地进行上述扩展。总之，这是第一次将非奇异核分数阶导数应用于分数阶忆阻器建模，并提出了具有完全显式记忆描述的结果模型。所提出的模型还具有高度通用性，适用于实际电路，并且可扩展到分数阶磁电抗。可以方便地进行上述扩展。总之，这是第一次将非奇异核分数阶导数应用于分数阶忆阻器建模，并提出了具有完全显式记忆描述的结果模型。所提出的模型还具有高度通用性，适用于实际电路，并且可扩展到分数阶磁电抗。可以方便地进行上述扩展。总之，这是第一次将非奇异核分数阶导数应用于分数阶忆阻器建模，并提出了具有完全显式记忆描述的结果模型。所提出的模型还具有高度通用性，适用于实际电路，并且可扩展到分数阶磁电抗。

更新日期：2022-08-22

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