Review of Some Promising Fractional Physical Models
By Vasily E. Tarasov. 2013
167 citations recorded by the source corpus.
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law nonlocality, power-law long-term memory or fractal properties by using integrations and differentiation of noninteger orders, i.e., by methods in the fractional calculus. This paper is a review of physical models that look very promising for future development of fractional dynamics. We suggest a short introduction to fractional calculus as a theory of integration and differentiation of noninteger order. Some applications of integro-differentiations of fractional orders in physics are discussed. Models of discrete systems with memory, lattice with long-range inter-particle interaction, dynamics of fractal media are presented. Quantum analogs of fractional derivatives and model of open nano-system systems with memory are also discussed.
Subfields: Modeling and Simulation, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/d53b7a7add5913233facd3f3d7e6b45410d56bd5
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Citations in the corpus
- New fractional integral unifying six existing fractional integrals (2016, unknown): “known in the literature as Weyl and Liouville type integrals, respectively. Such integrals are corresponding to infinite memory effects and have applications in financial mathematics and diffusion models [5, 33]. Let us note that, using the change of variable u= (τ/x)ρ, the integral (1) can be rewritten”
- Weighted Fractional Calculus: A General Class of Operators (2022, background): “Such generalisations are not only a pure mathematical curiosity, as differential equations involving the generalised operators have been applied in many scientific fields [4,5] ranging from viscoelasticity [6] to epidemiology [7] to economics [8,9] to electrical circuits [10].”