Results 31 to 40 of about 278,072 (286)

General Fractional Vector Calculus

Mathematics, 2021
A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators.
Vasily E. Tarasov
doaj   +1 more source

FRACTIONAL DYNAMICS IN FINANCIAL INDICES [PDF]

International Journal of Bifurcation and Chaos, 2012
The goal of this study is the analysis of the dynamical properties of financial data series from 32 worldwide stock market indices during the period 2000–2009 at a daily time horizon. Stock market indices are examples of complex interacting systems for which a huge amount of data exists.
Machado, J. A. Tenreiro, Duarte, Fernando B., Duarte, Gonçalo Monteiro   +2 more
openaire   +2 more sources

Fractional Fokker-Planck dynamics: Numerical algorithm and simulations [PDF]

, 2006
Anomalous transport in a tilted periodic potential is investigated numerically within the framework of the fractional Fokker-Planck dynamics via the underlying CTRW.
E. Heinsalu, G. H. Weiss, G. Schmid, I. Goychuk, J. A. Freund, M. Patriarca, P. Hänggi, R. Gorenflo, R. L. Stratonovich, R. L. Stratonovich, V. I. Tikhonov, W. Ebeling, W. H. Press, Yu. M. Ivanchenko, Yu. M. Ivanchenko   +14 more
core   +2 more sources

Fractal Properties of the Magnetic Polarity Scale in the Stochastic Hereditary αω-Dynamo Model

Fractal and Fractional, 2022
We study some fractal properties of the hereditary αω-dynamo model in the two-mode approximation. The phase variables of the model describe the temporal dynamics of the toroidal and poloidal components of the magnetic field.
Gleb Vodinchar , Lyubov Feshchenko
doaj   +1 more source

Photothermal Response for the Thermoelastic Bending Effect Considering Dissipating Effects by Means of Fractional Dual-Phase-Lag Theory

Fractal and Fractional, 2023
We analyze an extension of the dual-phase lag model of thermal diffusion theory to accurately predict the contribution of thermoelastic bending (TE) to the Photoacoustic (PA) signal in a transmission configuration.
Aloisi Somer, Andressa Novatski, Marcelo Kaminski Lenzi, Luciano Rodrigues da Silva, Ervin Kaminski Lenzi   +4 more
doaj   +1 more source

Periodically Kicked Rotator with Power-Law Memory: Exact Solution and Discrete Maps

Fractal and Fractional
This article discusses the transformation of a continuous-time model of the fractional system into a discrete-time model of the fractional system. For the continuous-time model, the exact solution of the nonlinear equation with fractional derivatives ...
Vasily E. Tarasov
doaj   +1 more source

A Fractional Computer Virus Propagation Model with Saturation Effect

Fractal and Fractional
The epidemic modeling of computer virus propagation is identified as an effective approach to understanding the mechanism of virus spread. Fraction-order virus spread models exhibit remarkable advantages over their integer-order counterparts.
Zijie Liu, Xiaofan Yang, Luxing Yang
doaj   +1 more source

Evolutionary Mathematical Science, Fractional Modeling and Artificial Intelligence of Nonlinear Dynamics in Complex Systems

Chaos Theory and Applications, 2022
Complex problems in nonlinear dynamics foreground the critical support of artificial phenomena so that each domain of complex systems can generate applicable answers and solutions to the pressing challenges.
Dumitru Baleanu, Yeliz Karaca
doaj  

General Fractional Calculus: Multi-Kernel Approach

Mathematics, 2021
For the first time, a general fractional calculus of arbitrary order was proposed by Yuri Luchko in 2021. In Luchko works, the proposed approaches to formulate this calculus are based either on the power of one Sonin kernel or the convolution of one ...
Vasily E. Tarasov
doaj   +1 more source

Universal Fractional Map and Cascade of Bifurcations Type Attractors

, 2013
We modified the way in which the Universal Map is obtained in the regular dynamics to derive the Universal $\alpha$-Family of Maps depending on a single parameter $\alpha > 0$ which is the order of the fractional derivative in the nonlinear fractional ...
Edelman, Mark
core   +1 more source