Fractional Integrals and Derivatives: Theory and Applications

By S. Samko, Anatoly A. Kilbas, O. Marichev. 1993

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Citations in the corpus

fPINNs: Fractional Physics-Informed Neural Networks (2018, background): “The definition of the Riemann-Liouville directional derivative of a sufficiently properly defined function w(x) is (α ∈ (1, 2)) [55, 48]”
Variational solution of fractional advection dispersion equations on bounded domains in ℝd (2007, methodology): “See [14] for a discussion on Finite Element implementation issues for FADEs.”
Numerical Study for the Fractional Differential Equations Generated by Optimization Problem Using Chebyshev Collocation Method and FDM (2013, background): “For more details on fractional derivatives definitions and their properties see ( [15], [24]).”
A numerical approach for solving a class of variable-order fractional functional integral equations (2018, background): “1993), plasma physics (Samko et al. 1993), or control problems (Das 2011; Dabiri et al.”
The fractional‐order governing equation of Lévy Motion (2000, background): “Defining the symmetric operator equivalent to the Riesz potential [Samko et al., 1993] : 2ٌ ␣ ϵ D ϩ ␣ ϩ D Ϫ ␣ (20) gives the mass balance equation for advection and symmetric fractional dispersion: ѨC Ѩt ϭ Ϫv ⅐ ٌC ϩ Ᏸٌ ␣ C. (21) We use the description " fractional ADE " with the understanding that…”
Symmetry properties of fractional diffusion equations (2009, unknown): “(11) One can see, using the generalized Leibnitz rule [4]”
Some generalized fractional calculus operators and their applications in integral equations (2012, background): “(1) Generalized fractional integrals with specific functions z(t) and with weights w(t) could be found in [12] and [6].”