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.

MSC:

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

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