Mittag-Leffler Functions, Related Topics and Applications

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fPINNs: Fractional Physics-Informed Neural Networks (2018, background): “The analytical forms of the space-fractional and the time-fractional derivatives of the fabricated solutions are given in [56] and [57], respectively.”
On the Ulam–Hyers–Rassias stability for nonlinear fractional differential equations using the $$\psi $$ψ-Hilfer operator (2017, neutral): “[37] (One parameter Mittag–Leffler function).”
Nonlocal boundary value problem for generalized Hilfer implicit fractional differential equations (2020, neutral): “y(0) = 0, (55) y(1) = 10 7  45 ; Ψ 0+ y (1 3 ) + 13 6  83 ; Ψ 0+ y (1 2 ) .”
Fundamental solutions of the general fractional‐order diffusion equations (2018, neutral): “LC 0 D (ν) τ ( τOν,υ (−τ) ) = τ2(υ−1)O ν,2υ−1 (−τ ) , (26)”
Some Properties of the Kilbas-Saigo Function (2020, background): “15) in [2], gives the reason the constant in the lower bound of Theorem 2 is optimal—see the above Remark 4 (a).”
Some New Fractional-Calculus Connections between Mittag–Leffler Functions (2019, background): “The above function with a single parameter α has also been extended to more general functions defined with two or more parameters, such as the following [15,16].”