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General Fractional Dynamics [PDF]
Mathematics, 2021 General fractional dynamics (GFDynamics) can be viewed as an interdisciplinary science, in which the nonlocal properties of linear and nonlinear dynamical systems are studied by using general fractional calculus, equations with general fractional ...
Vasily E. Tarasov
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Fractional Dynamics of HIV with Source Term for the Supply of New CD4+ T-Cells Depending on the Viral Load via Caputo–Fabrizio Derivative [PDF]
Molecules, 2021 Human immunodeficiency virus (HIV) is a life life-threatening and serious infection caused by a virus that attacks CD4+ T-cells, which fight against infections and make a person susceptible to other diseases.
Zahir Shah +4 more
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Why Do Big Data and Machine Learning Entail the Fractional Dynamics? [PDF]
Entropy, 2021 Fractional-order calculus is about the differentiation and integration of non-integer orders. Fractional calculus (FC) is based on fractional-order thinking (FOT) and has been shown to help us to understand complex systems better, improve the processing ...
Haoyu Niu, YangQuan Chen, Bruce J. West
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Optimal random search, fractional dynamics and fractional calculus [PDF]
Volume 4: 18th Design for Manufacturing and the Life Cycle Conference; 2013 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, 2013 What is the most efficient search strategy for the random located target sites subject to the physical and biological constraints? Previous results suggested the L\'evy flight is the best option to characterize this optimal problem, however, which ...
Chen, YangQuan, Zeng, Caibin
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Dynamics with Low-Level Fractionality [PDF]
Physica A: Statistical Mechanics and its Applications, 2005 The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and field theory.
Achar +55 more
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Fractional statistical dynamics and fractional kinetics
, 2016 We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum in terms of solutions to Vlasov-type hierarchies. As a by-product we obtain the evolution of the density of particles in the fractional kinetics in
da Silva, Jose Luis +2 more
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Rules for Fractional-Dynamic Generalizations: Difficulties of Constructing Fractional Dynamic Models [PDF]
Mathematics, 2019 This article is a review of problems and difficulties arising in the construction of fractional-dynamic analogs of standard models by using fractional calculus.
Vasily E. Tarasov
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Complex Systems and Fractional Dynamics. [PDF]
Entropy (Basel), 2018 Complex systems (CS) are pervasive in many areas of science and technology, namely in financialmarkets, transportation, telecommunication and social networks, world and country economies,immunological systems, living organisms, computational systems, and electrical and mechanicalstructures [...]
M Lopes A, Tenreiro Machado JA.
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Fractional-Time Schr\"odinger Equation: Fractional Dynamics on a Comb [PDF]
Chaos, Solitons & Fractals, 2011 The physical relevance of the fractional time derivative in quantum mechanics is discussed. It is shown that the introduction of the fractional time Scr\"odinger equation (FTSE) in quantum mechanics by analogy with the fractional diffusion $\frac{\prt ...
Iomin, Alexander
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