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Fractals and Fractional Calculus in Continuum Mechanics. Springer-Verlag Telos. ISBN 978-3-211-82913-4. Igor Podlubny (27 October 1998). Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Elsevier. ISBN 978-0-08-053198-4.
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 ...
Analysis on fractals or calculus on fractals is a generalization of calculus on smooth manifolds to calculus on fractals. ... Analysis on graphs and its applications: ...
The Koch snowflake (also known as the Koch curve, Koch star, or Koch island [1] [2]) is a fractal curve and one of the earliest fractals to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled "On a Continuous Curve Without Tangents, Constructible from Elementary Geometry" [3] by the Swedish mathematician Helge von Koch.
Fractal branching of trees. Fractal analysis is assessing fractal characteristics of data.It consists of several methods to assign a fractal dimension and other fractal characteristics to a dataset which may be a theoretical dataset, or a pattern or signal extracted from phenomena including topography, [1] natural geometric objects, ecology and aquatic sciences, [2] sound, market fluctuations ...
Like some other fractals, the function exhibits self-similarity: every zoom (red circle) is similar to the global plot. In mathematics, the Weierstrass function, named after its discoverer, Karl Weierstrass, is an example of a real-valued function that is continuous everywhere but differentiable nowhere. It is also an example of a fractal curve.
Mobile phone and Wi-Fi fractal antennas have been produced in the form of few iterations of the Sierpiński carpet. Due to their self-similarity and scale invariance, they easily accommodate multiple frequencies. They are also easy to fabricate and smaller than conventional antennas of similar performance, thus being optimal for pocket-sized ...
The history of fractals traces a path from chiefly theoretical studies to modern applications in computer graphics, with several notable people contributing canonical fractal forms along the way. [ 8 ] [ 9 ] A common theme in traditional African architecture is the use of fractal scaling, whereby small parts of the structure tend to look ...