Results 221 to 230 of about 1,105 (254)
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Construction of fractal calculus
SCIENTIA SINICA Mathematica, 2015A fractal function does not have the derivatives in Newton sense, however, it still represents some kind of motion and then certainly it has velocity (rate of change). How to construct fractal calculus in order to describe the velocity of a fractal function is a challenging and important problem.
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2017
Many real physical processes possess “memory,” which comes as follows: time connection between the process cause, f(t), and the process effect, g(t), is not immediate, and the condition of g(t) is specified with the condition of f(t) not at the same moment but delayed. This property is called hereditary.
Anis Kharisovich Gil’mutdinov +2 more
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Many real physical processes possess “memory,” which comes as follows: time connection between the process cause, f(t), and the process effect, g(t), is not immediate, and the condition of g(t) is specified with the condition of f(t) not at the same moment but delayed. This property is called hereditary.
Anis Kharisovich Gil’mutdinov +2 more
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THE RELATIONSHIP BETWEEN FRACTIONAL CALCULUS AND FRACTALS
Fractals, 1995The general relationship between fractional calculus and fractals is explored. Based on prior investigations dealing with random fractal processes, the fractal dimension of the function is shown to be a linear function of the order of fractional integro-differentiation.
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Fractional Calculus on Fractal Functions
2020The words fractional calculus were born from a communication between L’Hospital and Leibniz in 1695. By denoting the nth derivative of f with respect to x as \(\frac{d^nf}{dx^n}\), Leibniz had written a letter to L’Hospital. In his letter, Leibniz assumed that n takes the value from the positive integers, i.e., \(n\in \mathbb {N}\).
Santo Banerjee +2 more
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The Generic Nonlocal Fractal Calculus
2022The generic nonlocal fractal calculus scheme have been formulated in this work. A unified derivative operator which employs an interpolated characteristic between the generic nonlocal derivative in Riemann–Liouville and Caputo senses has also been derived. For being generic, an arbitrary kernel function has been adopted.
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Fractal Frenet equations for Fractal curves: a fractal calculus approach
Boletín de la Sociedad Matemática MexicanaThe formulation of Fractal Frenet equations, which are differential equations intended to characterize the geometric behavior of vector fields along fractal curves, is presented in this study. It offers a framework for calculating the length of such irregular curves by introducing a fractal analogue of arc length.
Alireza Khalili Golmankhaneh +2 more
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CALCULUS ON FRACTAL SUBSETS OF REAL LINE — II: CONJUGACY WITH ORDINARY CALCULUS
Fractals, 2011Calculus on fractals, or Fα-calculus, developed in a previous paper, is a calculus based fractals F ⊂ R, and involves Fα-integral and Fα-derivative of orders α, 0 < α ≤ 1, where α is the dimension of F. The Fα-integral is suitable for integrating functions with fractal support of dimension α, while the Fα-derivative enables us to differentiate ...
Parvate, Abhay, Gangal, A. D.
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A note on Katugampola fractional calculus and fractal dimensions
Applied Mathematics and Computation, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Saurabh Verma, P. Viswanathan
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