Generalized Taylor’s formula. (English) Zbl 1122.26006

Odibat, Zaid M.; Shawagfeh, Nabil T.

Appl. Math. Comput. 186, No. 1, 286-293 (2007).

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.

Reviewer: S. L. Kalla (Kuwait)

MSC:

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

Keywords:

fractional integral; Caputo fractional derivative

Citations:

Zbl 0063.01925; Zbl 0931.26004; JFM 57.0477.02

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