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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 approaches fail to factor in the fractal nature of the media. A Hausdorff measure, fractal measure ''t'' is scaled according to ''tα''. Such a derivative is local, in contrast to the similarly applied fractional derivative. Fractal calculus is formulated as a generalization of standard calculus. Physical background 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 Fick's laws of diffusion, Darcy's law, and Fourier's law) are not applicable to fractal media. To address this, concepts such as distance and velocity mu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applied Mathematics
Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the profession, professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics. History Historically, applied mathematics consisted principally of Mathematical analysis, applied analysis, most notably differential equations; approximation theory (broadly construed, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
