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.