Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media

By V. E. Tarasov. 2011

1,544 citations recorded by the source corpus.

Subfields: Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d07e160286a750ee9a1d2f9cb491562110453972

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In Statistical and Nonlinear Physics

Citations in the corpus

A new fractional operator of variable order: Application in the description of anomalous diffusion (2016, positive): “Fractional-order derivatives (FOD) of the Riemann-Liouville and Caputo types with respect to the power-law-function kernel [1,2,3,4] are important for developing mathematical models in the areas of the control, nuclear physics, electrical circuits, signal processing, economy and biology.”
Fractional Calculus: Quo Vadimus? (Where are we Going?) (2015, result): “We have taken the present occasion, as a compliment to our previous survey [107], to cite books published during the years 2011 [92, 80, 44, 26, 65, 47, 5, 106, 117], 2012 [7, 3, 77, 1, 51, 38, 102, 56, 122, 15, 112, 110, 118], 2013 [14, 18, 89, 29, 36], and 2014 [57, 4, 121, 39, 105, 40, 66, 86, 2,”
Local fractional series expansion method for solving wave and diffusion equations on Cantor sets (2013, positive): “Introduction Fractional calculus theory [1–3] has been applied to a wide class of complex problems encompassing physics, biology, mechanics, and interdisciplinary areas [4–9].”
On chain rule for fractional derivatives (2016, background): “and these operators have wide applications in physics and mechanics (for example, see [9] and references therein).”
Existence and Ulam stability for nonlinear implicit fractional differential equations with Hadamard derivative (2017, background): “We refer the reader, for example, to the books such as [6, 18, 20, 22, 30], and references therein.”