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Zbl 1122.26006
Odibat, Zaid M.; Shawagfeh, Nabil T.
Generalized Taylor's formula. (English)
[J] Appl. Math. Comput. 186, No. 1, 286-293 (2007). ISSN 0096-3003

The ordinary Taylor's formula has been generalized by several authors [{\it G. Hardy}, J. Lond. Math. Soc. 20, 48--57 (1945; Zbl 0063.01925); {\it J. J. Trujillo, M. Rivero} and {\it B. Bonilla}, J. Math. Anal. 231, No. 1, 255--265 (1999; Zbl 0931.26004); {\it 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.
[S. L. Kalla (Kuwait)]

MSC 2000:: *26A33 Fractional derivatives and integrals (real functions)
33C60 Hypergeometric integrals and functions defined by them

Keywords: fractional integral; Caputo fractional derivative

Citations: Zbl 0063.01925; Zbl 0931.26004; JFM 57.0477.02

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