On the fractional Cornu spirals

Milici, Constantin; Machado, J. A. Tenreiro; Drăgănescu, Gheorghe

doi:10.1016/j.cnsns.2018.07.004

Cited by 4 publications

(2 citation statements)

References 12 publications

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“…In addition to its use in optics, the Cornu spiral has also found use in highway design [27], Kloosterman paths [28], and Van der Corput transforms [29]. Very recently Milici et al [30] have studied fractional Cornu spirals via the machinery of fractional calculus.…”

Section: Fresnel Integrals and The Cornu Spiralmentioning

confidence: 99%

Cornu Spirals and the Triangular Lacunary Trigonometric System

Vogt

Ulness

2019

Fractal Fract

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This work is intended to directly supplement the previous work by Coutsias and Kazarinoff on the foundational understanding of lacunary trigonometric systems and their relation to the Fresnel integrals, specifically the Cornu spirals [Physica 26D (1987) 295]. These systems are intimately related to incomplete Gaussian summations. The current work provides a focused look at the specific system built off of the triangular numbers. The special cyclic character of the triangular numbers modulo m carries through to triangular lacunary trigonometric systems. Specifically, this work characterizes the families of Cornu spirals arising from triangular lacunary trigonometric systems. Special features such as self-similarity, isometry, and symmetry are presented and discussed.

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Section: Fresnel Integrals and The Cornu Spiralmentioning

confidence: 99%

Cornu Spirals and the Triangular Lacunary Trigonometric System

Vogt

Ulness

2019

Fractal Fract

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“…Generally speaking, fractional applications are formulated according to a more complex model than an integer one, so to obtain information about the geometry of the model, they can be plotted and the corresponding model analyzed. This approach is given by milici and Machado, [34]. In [35,36], Has et al investigated the many special curves by using conformable fractional derivatives.…”

Section: Introductionmentioning

confidence: 99%

Fractional approach to evolution of the magnetic field lines near the magnetic null points

Durmaz,

Özdemir,

Sekerci

2024

Phys. Scr.

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In this work, the magnetic reconnection model near null points in 3D space will be investigated using fractional calculations in the 3D magnetohydrodynamic framework. For the initial magnetic configuration (without external currents), we reformulated the numerically solved boundary initial value problem using fractional calculations. We studied the 3D Magnetic reconnection states and the behavior of the magnetic field around the null point and the null line. We also analyzed the fractional significance of charged particle motions in Killing magnetic fields. Moreover, the obtained results were visualized, and a comparison was made between the results obtained from integer and fractional calculations.

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The spirals of the Slope Chain Code

Bribiesca

2019

Pattern Recognition

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On the fractional Cornu spirals

Cited by 4 publications

References 12 publications

Cornu Spirals and the Triangular Lacunary Trigonometric System

Cornu Spirals and the Triangular Lacunary Trigonometric System

Fractional approach to evolution of the magnetic field lines near the magnetic null points

The spirals of the Slope Chain Code

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