Grunwald-Letnikov Derivative: Analysis in Range of First Order

Cioć, R.

doi:10.2174/9781681085999118010010

Cited by 3 publications

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“…The interpretations of G-L differintegral are shown in [7] but they have borders due to the possibility of substitution of any number for η and properties of gamma function. This problem is shown in the work [8]. lem but ing me for 2. where: p = t 0 ¡ t n dt .…”

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confidence: 93%

Bulletin of the Polish Academy of Sciences: Technical Sciences

Cioć,

Chrzan

2019

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The paper presents an interpretation of fractional calculus for positive and negative orders of functions based on sampled measured quantities and their errors connected with digital signal processing. The derivative as a function limit and the Grünwald-Letnikov differintegral are shown in chapter 1 due to the similarity of the presented definition. Notation of fractional calculus based on the gradient vector of measured quantities and its geometrical and physical interpretation of positive and negative orders are shown in chapters 2 and 3.

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confidence: 93%

Bulletin of the Polish Academy of Sciences: Technical Sciences

Cioć,

Chrzan

2019

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“…Furthermore, e.g., in the Grünwald-Letnikov definition, there is an inaccuracy in the record with a constant number of iterations and any value of the order [6]. There are no additional assumptions for the derivative here and it cannot be clearly interpreted so that it has a physical sense [7]. The problems that are mentioned above do not apply to the fractional definitions: Caputo, CFD and CFD in the Caputo sense.…”

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confidence: 99%

Analysis of an Electrical Circuit Using Two-Parameter Conformable Operator in the Caputo Sense

Piotrowska

Sajewski

2021

Symmetry

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The problem of voltage dynamics description in a circuit containing resistors, and at least two fractional order elements such as supercapacitors, supplied with constant voltage is addressed. A new operator called Conformable Derivative in the Caputo sense is used. A state solution is proposed. The considered operator is a generalization of three derivative definitions: classical definition (integer order), Caputo fractional definition and the so-called Conformable Derivative (CFD) definition. The proposed solution based on a two-parameter Conformable Derivative in the Caputo sense is proven to be better than the classical approach or the one-parameter fractional definition. Theoretical considerations are verified experimentally. The cumulated matching error function is given and it reveals that the proposed CFD–Caputo method generates an almost two times lower error compared to the classical method.

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