Results 11 to 20 of about 224,342 (242)
Fractal Calculus on Fractal Interpolation Functions [PDF]
Fractal and Fractional, 2021 In this paper, fractal calculus, which is called Fα-calculus, is reviewed. Fractal calculus is implemented on fractal interpolation functions and Weierstrass functions, which may be non-differentiable and non-integrable in the sense of ordinary calculus.
Alireza K. Golmankhaneh +2 more
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Fractal Continuum Calculus of Functions on Euler-Bernoulli Beam
Fractal and Fractional, 2022 A new approach for solving the fractal Euler-Bernoulli beam equation is proposed. The mapping of fractal problems in non-differentiable fractals into the corresponding problems for the fractal continuum applying the fractal continuum calculus (FdH3-CC ...
Andriy Kryvko +2 more
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The Fractal Calculus for Fractal Materials
Fractal and Fractional, 2019 The major problem in the process of mixing fluids (for instance liquid-liquid mixers) is turbulence, which is the outcome of the function of the equipment (engine). Fractal mixing is an alternative method that has symmetry and is predictable.
Amir Pishkoo, Mohammad Sadegh Asgari
exaly +4 more sources
A numerical framework for fractional and fractal-fractional analysis of the Pehlivan chaotic system using Caputo derivative [PDF]
Scientific ReportsThe Pehlivan chaotic system, introduced by Ibrahim Pehlivan and Yilmaz Uyaroglu, is a three-dimensional autonomous chaotic model with rich dynamical properties.
R. Vinoth, M. Jayalakshmi
doaj +2 more sources
Fractal calculus and its geometrical explanation
Results in Physics, 2018 Fractal calculus is very simple but extremely effective to deal with phenomena in hierarchical or porous media. Its operation is almost same with that by the advanced calculus, making it much accessible to all non-mathematicians.
Ji-Huan He
exaly +3 more sources
Fractal Sturm–Liouville Theory
Fractal and FractionalThis paper provides a short summary of fractal calculus and its application to generalized Sturm–Liouville theory. It presents both the fractal homogeneous and non-homogeneous Sturm–Liouville problems and explores the theory’s applications in optics.
Alireza Khalili Golmankhaneh +3 more
doaj +2 more sources
Economic models involving time fractal [PDF]
Mathematics and Modeling in Finance, 2021 In this article, the price adjustment equation has been proposed and studied in the frame of fractal calculus which plays an important role in market equilibrium.
Alireza Khalili Golmankhaneh +3 more
doaj +1 more source
Bounds on the hausdorff dimension of a renormalisation map arising from an excitable reaction-diffusion system on a fractal lattice [PDF]
, 2008 A renormalisation approach to investigate travelling wave solutions of an excitable reaction- diusion system on a deterministic fractal structure has recently been derived.
Mulholland, A.J.
core +4 more sources
Tsallis entropy on fractal sets
Journal of Taibah University for Science, 2021 In this article, we review fractal calculus ( $ F^{\alpha } $ -calculus) and define generalized Tsallis entropy on the fractal sets which is called fractal Tsallis entropy.
Alireza Khalili Golmankhaneh
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Fractal and Fractional, 2022 In this study, the variable order fractional calculus of the hidden variable fractal interpolation function is explored. It extends the constant order fractional calculus to the case of variable order. The Riemann–Liouville and the Weyl–Marchaud variable
Valarmathi Raja, Arulprakash Gowrisankar
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