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Fractional Dynamics

, 2015
The book is devoted to recent developments in the theory of fractional calculus and its applications. Particular attention is paid to the applicability of this currently popular research field in various branches of pure and applied mathematics. In particular, the book focuses on the more recent results in mathematical physics, engineering applications,
Srivastava, Hari M., Cattani, Carlo, Yang, Xiao-Jun   +2 more
openaire   +3 more sources

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

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

Dynamics with low-level fractionality [PDF]

Physica A: Statistical Mechanics and its Applications, 2006
LaTeX, 24 pages, to be published in Physica ...
Tarasov, Vasily E., Zaslavsky, George M.
openaire   +2 more sources

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

An application of fractional calculus to dielectric relaxation processes

, 2012
Recently fractional calculus has been successfully applied in the description of complex dynamics and proved to be a valuable tool for the solution of non-linear differential equations.
Çavuş M., Bozdemir S.
core   +1 more source

Analysis of Fractional Dynamic Systems [PDF]

The Scientific World Journal, 2014
Due to the extensive applications of fractional differential equations (FDEs) in engineering and science, research in this area has grown significantly. Fractional Dynamic Systems are described by FDEs, and this special issue consists of 8 original articles covering various aspects of FDEs and their applications written by prominent researchers in the ...
Fawang Liu, Richard Magin, Changpin Li, Alla Sikorskii, Santos Bravo Yuste   +4 more
openaire   +3 more sources

General Non-Local Continuum Mechanics: Derivation of Balance Equations

Mathematics, 2022
In this paper, mechanics of continuum with general form of nonlocality in space and time is considered. Some basic concepts of nonlocal continuum mechanics are discussed. General fractional calculus (GFC) and general fractional vector calculus (GFVC) are
Vasily E. Tarasov
doaj   +1 more source