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- W2803647811 abstract "In this paper we use the asymptotic expansions of the binomial coefficients and the weights of the L1 approximation to obtain approximations of order $2-alpha$ and second-order approximations of the Caputo derivative by modifying the weights of the shifted Grunwald-Letnikov difference approximation and the L1 approximation of the Caputo derivative. A modification of the shifted Grunwald-Letnikov approximation is obtained which allows second-order numerical solutions of fractional differential equations with arbitrary values of the solutions and their first derivatives at the initial point." @default.
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- W2803647811 date "2018-06-09" @default.
- W2803647811 modified "2023-10-13" @default.
- W2803647811 title "Asymptotic expansions and approximations for the Caputo derivative" @default.
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- W2803647811 doi "https://doi.org/10.48550/arxiv.1806.03421" @default.
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