Approximating fractional derivative of Faddeeva function, Gaussian function, and Dawson's integral

Yarman, Can Evren

doi:10.1002/mma.5679

Cited by 6 publications

(4 citation statements)

References 26 publications

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“…As these results show, the envelope of the output signal in the time domain has two “lobes” which are asymmetrical around the central dip (i.e., the lobes have different amplitudes and temporal duration), compared to the first order differentiation case presented in Fig. 3 .This asymmetric temporal signal is an expected feature of fractional derivatives with of Gaussian signals 63 , 64 . These results demonstrate that the proposed structure indeed has the ability to perform fractional differentiation onto the incident temporal signal.…”

Section: Resultsmentioning

confidence: 65%

Time derivatives via interconnected waveguides

Glyn MacDonald,

Yakovlev,

Pacheco-Peña

2023

Sci Rep

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Electromagnetic wave-based analogue computing has become an interesting computing paradigm demonstrating the potential for high-throughput, low power, and parallel operations. In this work, we propose a technique for the calculation of derivatives of temporal signals by exploiting transmission line techniques. We consider multiple interconnected waveguides (with some of them being closed-ended stubs) forming junctions. The transmission coefficient of the proposed structure is then tailored by controlling the length and number of stubs at the junction, such that the differentiation operation is applied directly onto the envelope of an incident signal sinusoidally modulated in the time domain. The physics behind the proposed structure is explained in detail and a full theoretical description of this operation is presented, demonstrating how this technique can be used to calculate higher order or even fractional temporal derivatives. We envision that these results may enable the development of further time domain wave-based analogue processors by exploiting waveguide junctions, opening new opportunities for wave-based single operators and systems.

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Section: Resultsmentioning

confidence: 65%

Time derivatives via interconnected waveguides

Glyn MacDonald,

Yakovlev,

Pacheco-Peña

2023

Sci Rep

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“…It is common to find the limit of a function in the limit of a composite function. Like the derivation of a composite function is often transformed into the derivation of a simple function using the law of derivation of composite functions, the limit of a composite function is often transformed into the limit of a simple function [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

A method for solving the limit of multivariate composite functions

Liang,

Wang

2024

Applied Mathematics and Nonlinear Sciences

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In this paper, according to the concept of multivariate composite function, the limit and continuity conditions of multivariate composite function are given, and the continuity relationship between the inner function and the outer function of the composite function at the same point is investigated. The relationship between the limit and continuity of a composite function composed of two functions at the same point is investigated by examples, while some limit results are explained from the perspective of composite functions, and the limit calculation law of multivariate composite functions is proposed. Using the consistent central limit theorem in the limit calculation law, the absolute value and limit of the interval of the multivariate composite function are obtained, and the iterative limit of the variational reduction approximation method is confirmed by combining the absolute value and limit of the interval of the multivariate composite function. On the basis of the application of limit operation of a multivariate composite function, the limit distribution of high-dimensional likelihood ratio statistics of multivariate composite function is analyzed by using data simulation analysis. The results show that both limit distributions have better simulation results when p are small, such as p = 5 or p = 10, but the traditional limit is better than the normal limit, indicating that the results of multivariate composite function limit calculations have good accuracy. A method for solving the limits of multivariate composite functions is proposed in this study, which is of great theoretical and practical significance in the study of higher mathematics.

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“…Damped oscillator with fractional derivative has been also the objective of some studies, see [5]. Some extensions of the theory to other classical systems have been proposed, see for instance [6] and references therein, or in [8].…”

Section: Introductionmentioning

confidence: 99%

Approximate solutions of one-dimensional systems with fractional derivative

Ferrari

Gadella

Lara

et al. 2020

Int. J. Mod. Phys. C

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The fractional calculus is useful to model non-local phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution of ordinary fractional differential equations. Due to the non-locality of the fractional derivative, we may establish an equivalence between fractional oscillators and ordinary oscillators with a dissipative term.

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Approximating fractional derivative of Faddeeva function, Gaussian function, and Dawson's integral

Cited by 6 publications

References 26 publications

Time derivatives via interconnected waveguides

Time derivatives via interconnected waveguides

A method for solving the limit of multivariate composite functions

Approximate solutions of one-dimensional systems with fractional derivative

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