Journal
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
Volume 30, Issue 3, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218348X22500542
Keywords
Hausdorff Vector Calculus; Chen Hausdorff Calculus; Fractal Power-Law Flow; Anomalous Diffusion Equation; Navier-Stokes Equation
Funding
- China University of Mining and Technology [102504180004]
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In this paper, we propose the Hausdorff vector calculus based on the Chen Hausdorff calculus for the first time. The Gauss-Ostrogradsky-like, Stokes-like, and Green-like theorems, and Green-like identities are obtained in the framework of the Hausdorff vector calculus. A conjecture for the fractal power-law flow equations analogous to the Smale's 15th problem and one of Millennium Prize Problems for the Navier-Stokes equations is also addressed.
In the paper, we suggest the Hausdorff vector calculus based on the Chen Hausdorff calculus for the first time. The Gauss-Ostrogradsky-like, Stokes-like, and Green-like theorems, and Green-like identities are obtained in the framework of the Hausdorff vector calculus. The formula is proposed as a mathematical tool to describe the real-world problems for the fractal power-law flow equations with the anomalous diffusion equation. A conjecture for the fractal power-law flow equations analogous to the Smale's 15th problem and one of Millennium Prize Problems for the Navier-Stokes equations is also addressed.
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