Fractional Derivatives for Physicists and Engineers

By V. Uchaikin. 2013

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Citations in the corpus

fPINNs: Fractional Physics-Informed Neural Networks (2018, background): “Among these are solute transport in fractured and porous media [2, 3], acoustic wave propagation with frequency-dependent dissipation [4, 5, 6, 7], laminar and turbulent flows [8, 9, 10], viscoelastic constitutive laws [11], just to mention a few.”
Well-posedness of general Caputo-type fractional differential equations (2018, background): “Introduction Fractional calculus has already become a powerful and effective tool in describing the complex nonlinear phenomena arising in continuum mechanics, thermodynamics, plasma dynamics, quantum mechanics, electrodynamics and so on (see [23]).”
Conservation laws for time-fractional subdiffusion and diffusion-wave equations (2014, unknown): “, [38,39,52–54]).”
General conformable fractional derivative and its physical interpretation (2017, background): “Heredity and nonlocality are typical properties of these definitions [18], which are important in many application fields and are different from classical Newton–Leibniz calculus.”
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,”
Numerical Approaches to Fractional Integrals and Derivatives: A Review (2020, background): “electrodynamics, quantum mechanics, plasma dynamics, and cosmic rays [27].”