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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.
Analysis on fractals or calculus on fractals is a generalization of calculus on smooth manifolds to calculus on fractals. The theory describes dynamical phenomena which occur on objects modelled by fractals.
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.
Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.
The Newton fractal is a boundary set in the complex plane which is characterized by Newton's method applied to a fixed polynomial p(z) ∈ [z] or transcendental function. It is the Julia set of the meromorphic function z ↦ z − p ( z ) / p′ ( z ) which is given by Newton's method.