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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.
Differential Equations on Fractals. Princeton. ISBN 978-0-691-12542-8. Pavel Exner; Jonathan P. Keating; Peter Kuchment; Toshikazu Sunada & Alexander Teplyaev (2008). Analysis on graphs and its applications: Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, January 8-June 29, 2007. AMS Bookstore. ISBN 978-0-8218-4471-7.
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 ...
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 ...
By applying a Laplace transform to the LTI system above, the transfer function becomes = () = = =For general orders and this is a non-rational transfer function. Non-rational transfer functions cannot be written as an expansion in a finite number of terms (e.g., a binomial expansion would have an infinite number of terms) and in this sense fractional orders systems can be said to have the ...
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 ...
Fractal fern in four states of construction. Highlighted triangles show how the half of one leaflet is transformed to half of one whole leaf or frond.. Though Barnsley's fern could in theory be plotted by hand with a pen and graph paper, the number of iterations necessary runs into the tens of thousands, which makes use of a computer practically mandatory.