2013/03/25 by Vasily E. Tarasov
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Applied mathematics #Calculus (dental) #Fractal #Fractional Differential Equations Solutions #Fractional calculus #Lattice (music) #Mathematical analysis #Mathematics #Physical system #Physics #Quantum #Quantum mechanics #Quantum nonlocality #Statistical Mechanics and Entropy #Statistical physics #physics.gen-ph
paper · pdf · doi:10.1142/s0217979213300053
published as International Journal of Modern Physics B. Vol.27. No.9. (2013) 1330005 · 38 pages, LaTeX
openalex publication_date 2013/03/25 · arxiv created 2015/02/14 · arxiv updated 2015/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 non-integer 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.