Hausdorff fractal derivative
In applied mathematics and mathematical analysis, the fractal derivative or Hausdorff derivative is a non-Newtonian generalization of the derivative dealing with the measurement of fractals, defined in fractal geometry. Fractal derivatives were created for the study of anomalous diffusion, by which traditional … See more Porous media, aquifers, turbulence, and other media usually exhibit fractal properties. Classical diffusion or dispersion laws based on random walks in free space (essentially the same result variously known as See more The fractal derivative is connected to the classical derivative if the first derivative of the function under investigation exists. In this case, See more • Fractal analogue of the right-sided Riemann-Liouville fractional integral of order $${\displaystyle \beta \in \mathbb {R} }$$ of f is defined by: See more Based on above discussion, the concept of the fractal derivative of a function u(t) with respect to a fractal measure t has been introduced as follows: See more As an alternative modeling approach to the classical Fick's second law, the fractal derivative is used to derive a linear anomalous transport-diffusion equation underlying See more • Fractional calculus • Fractional-order system • Multifractal system See more • Power Law & Fractional Dynamics • Non-Newtonian calculus website See more WebThis paper makes the first attempt to employ the Hausdorff derivative Laplacian operator to sharpen the images. In terms of the visual quality of details, contours and edges, the …
Hausdorff fractal derivative
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WebIn mathematics, Hausdorff measure is a generalization of the traditional notions of area and volume to non-integer dimensions, specifically fractals and their Hausdorff dimensions.It is a type of outer measure, named for Felix Hausdorff, that assigns a number in [0,∞] to each set in or, more generally, in any metric space.. The zero-dimensional … Webspace derivatives. In this paper, a new Hausdorff fractal model is presented to characterize the non-Fickian solute transport in heterogeneous porous media. The …
WebDec 31, 2024 · A time-space Hausdorff derivative model for anomalous transport in porous media Download PDF. Download PDF. Research Paper; Published: 31 December 2024; A time-space Hausdorff derivative model for anomalous transport in porous media ... H. Sun, Z. Li, Y. Zhang, W. Chen, Fractional and fractal derivative models for transient … WebJul 11, 2024 · The Hausdorff fractal derivative, which is designed to characterize anomalous transport in fractal media, has intrinsic relationship with the fractal dimension of the medium. Meanwhile, fractal properties of river-bed structure have been widely investigated while interpreting bed-load transport [ 29 , 31 ].
WebHasselblatt and Schmeling stated in [9]2 the following Conjecture. The fractal dimension of a hyperbolic set is the sum of those of its stable and unstable slices, where ”fractal” can mean either Hausdorff or upper box dimension. For solenoids, in [9] and here, an affirmative answer on Hausdorff dimen- sion has been proven. WebDec 5, 2016 · Fractal derivative and operator In this article, we employ the definition of Hausdorff fractal derivative defined by Chen.30 Definition 1. Fractal derivative df(t) dta = lim t!t0 f(t) f(t0) ta t0a ð1Þ where a is the order of fractal derivative, represented a fractal measure; t denotes the coordinate in time. We
WebAug 6, 2024 · The purpose of this paper is to present a fractal model of the NNVS based on the Hausdorff fractal derivative fundamental concept. Design/methodology/approach. A two-scale transformation is used to convert the proposed fractal model into regular NNVS. The variational strategy of well-known Chinese scientist Prof. Ji Huan He is used to …
praxis glaser berlinWebThe fundamental solution of the three-dimensional Hausdorff derivative diffusion equation is closely related to scaling transform and non-Euclidean Hausdorff fractal distance. … praxis giese rathenowWeb5.5 Fractal Type. In applied mathematics and mathematical analysis, the fractal derivative is a nonstandard type of derivative in which the variable such as t has been scaled … praxis glaser hildenWebInterconnections and equivalence of the metric derivatives was presented in Reference —particularly between definitions of fractal derivatives, called Hausdorff derivative in Reference , q-derivatives in Reference , and conformable derivatives in Reference . Therein, a simple scale change in the variable was used to show that for ... praxis glaserWebAug 1, 2015 · Then the fractal dimension IV of F is defined by dim Γ 4 ( F) = inf { s: H 4 s ( F) = 0 } = sup { s: H 4 s ( F) = ∞ }. To simplify the notation, in this paper we will write dim … praxis gifted education practice testWebAug 21, 2024 · Because the Hausdorff fractal derivative is a local operator while the fractional derivative is a global operator. 5. Conclusions. This study establishes a HADE … scientific water namesWebJan 1, 2024 · The Hausdorff derivative involving the fractal geometry with the Hausdorff measure, proposed by Chinese mathematician Wen Chen [1,2], has played an important role in the treatment for the ... scientific visualization physics job