Hausdorff fractal derivative

Author: pzyb

August undefined, 2024

WebJan 18, 2024 · Cai W Chen W Wang F Three-dimensional Hausdorff derivative diffusion model for isotropic/anisotropic fractal porous media Therm Sci 2024 22 1 1 6 10.2298/TSCI170630265C ... Khan Y Faraz N Alsulaimani HA Two core optical fibers coupled nonlinear model in the framework of Hausdorff fractal derivative Results Phys … WebIt should be mentioned also that the Hausdorff fractal derivative proposed by Chen in [154,155,156] and defined on the non-Euclidean fractal metrics using a time-space scaling transform is consistent with LOSA where the space dimensionality is the dimension of the fractal. The Hausdorff derivative proposed by Chen is considered as an effective ...

(PDF) Hausdorff Calculus: Applications to Fractal Systems

WebLangmuir waves propagate in fractal complex plasma with fractal characteristics, which may cause some plasma particles to be trapped or causes wave turbulences. This phenomenon appears in the form of fractional order equations. Using an effective unified solver, some new solitary profiles such as rational, trigonometrically and hyperbolical … WebThis study aims at combining the machine learning technique with the Hausdorff derivative to solve one-dimensional Hausdorff derivative diffusion equations. In the proposed artificial neural network method, the multilayer feed-forward neural network is chosen and improved by using the Hausdorff derivative to the activation function of hidden ... shorewood 508

Fractal Fract Free Full-Text A Tuning Method via Borges Derivative …

Webspace derivatives. In this paper, a new Hausdorff fractal model is presented to characterize the non-Fickian solute transport in heterogeneous porous media. The … WebAug 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 … WebThe fundamental solution of the three-dimensional Hausdorff derivative diffusion equation is closely related to scaling transform and non-Euclidean Hausdorff fractal distance. The used method, as a meshless technique, is simple, accurate and efficient for solving the partial differential equations with fundamental solutions. shorewood 60404

On the Physical Fractional Modulations on Langmuir Plasma …

(PDF) Three-dimensional Hausdorff derivative diffusion …

WebJul 22, 2024 · The fundamental solutions of the integer-order and Hausdorff derivative diffusion have been widely discussed and applied in numerical investigation of diffusion behaviors [24, 25].In this section, the fundamental solutions for temporal and spatial structural derivative advection–dispersion models are derived under the consideration of … WebAug 1, 2015 · Unlike previous studies using fractional order derivatives, here the fractal derivative order is directly connected to the Hausdorff fractal dimension of the diffusion trajectory. The result is a simpler, computationally faster, and more direct way to incorporate tissue complexity and microstructure into the diffusional dynamics. shorewood 508 hilton headWebThis 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 original images and noisy images were sharpened by using an appropriate Hausdorff derivative order. Numerical results indicate that the Hausdorff derivative Laplacian ... sandwich arts society

"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 " - Hausdorff fractal derivative

(PDF) Hausdorff Calculus: Applications to Fractal Systems

Fractal Fract Free Full-Text A Tuning Method via Borges Derivative …

Hausdorff fractal derivative

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