Generalized Taylor’s formula. (English) Zbl 1122.26006

The ordinary Taylor’s formula has been generalized by several authors [G. Hardy, J. Lond. Math. Soc. 20, 48–57 (1945; Zbl 0063.01925); J. J. Trujillo, M. Rivero and B. Bonilla, J. Math. Anal. 231, No. 1, 255–265 (1999; Zbl 0931.26004); Y. Watanabe, Tôhoku Math. J. 34, 28–41 (1931; JFM 57.0477.02)]. In this paper the authors obtain a generalized Taylor’s formula, using Caputo fractional derivative. Some applications involving approximation of functions and solutions of fractional differential equations are given.


26A33 Fractional derivatives and integrals
33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
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