Results 21 to 30 of about 224,342 (242)
Fractal and Fractional, 2023 Fractional calculus (FC) has recently received increasing attention due to its applications in many fields involving complex and nonlinear systems. However, one of the key challenges in using FC to deal with fractal or multifractal phenomena is how to ...
Qiuming Cheng
doaj +1 more source
Energy-optimal steering of transitions through a fractal basin boundary. [PDF]
, 2004 We study fluctuational transitions in a discrete dy- namical system having two co-existing attractors in phase space, separated by a fractal basin boundary. It is shown that transitions occur via a unique ac- cessible point on the boundary.
Luchinsky, D. G. +3 more
core +4 more sources
Fuzzification of Fractal Calculus [PDF]
, 2023 In this manuscript, fractal and fuzzy calculus are summarized. Fuzzy calculus in terms of fractal limit, continuity, its derivative, and integral are formulated.
Serpa, Cristina +3 more
core +1 more source
Fractal Continuum Mapping Applied to Timoshenko Beams
Mathematics, 2023 In this work, a generalization of the Timoshenko beam theory is introduced, which is based on fractal continuum calculus. The mapping of the bending problem onto a non-differentiable self-similar beam into a corresponding problem for a fractal continuum ...
Didier Samayoa +4 more
doaj +1 more source
FRACTAL RADIOPHYSICS. Part 3. FRACTIONAL CALCULUS IN ELECTRODYNAMICS [PDF]
Radio Physics and Radio AstronomySubject and Purpose. At the beginning of the 21st century, a fundamentally new scientific direction was formed, currently known as fractal radiophysics.
O. V. Lazorenko, L. F. Chernogor
doaj +1 more source
Quantum Behavior Arises Because Our Universe is a Fractal [PDF]
Reports in Advances of Physical Sciences, 2017 To explain the origin of quantum behavior, we propose a fractal calculus to describe the non-local property of the fractal curve [Y. Tao, J. Appl. Math. 2013 (2013) 308691]. This study demonstrates that if the dimension of time axis is slightly less than
Yong Tao
doaj +1 more source
About Kepler’s Third Law on fractal-time spaces
Ain Shams Engineering Journal, 2018 In this paper, a mathematical model for fractal-time space is given involving Fα-calculus. Differential equations corresponding of the free fall motion and simple harmonic oscillator on fractal-time space are given and solved.
Alireza K. Golmankhaneh
doaj +1 more source
Fractal and Fractional, 2023 In this study, we delve into the general theory of operator kernel functions (OKFs) in operational calculus (OC). We established the rigorous mapping relation between the kernel function and the corresponding operator through the primary translation ...
Xiaobin Yu, Yajun Yin
doaj +1 more source
Random Variables and Stable Distributions on Fractal Cantor Sets
Fractal and Fractional, 2019 In this paper, we introduce the concept of fractal random variables and their related distribution functions and statistical properties. Fractal calculus is a generalisation of standard calculus which includes function with fractal support.
Alireza Khalili Golmankhaneh +1 more
doaj +1 more source
Fractal Stochastic Processes on Thin Cantor-Like Sets
Mathematics, 2021 We review the basics of fractal calculus, define fractal Fourier transformation on thin Cantor-like sets and introduce fractal versions of Brownian motion and fractional Brownian motion. Fractional Brownian motion on thin Cantor-like sets is defined with
Alireza Khalili Golmankhaneh +1 more
doaj +1 more source