Generalized Taylor's formula
The ordinary Taylor's formula has been generalized by several authors [\textit{G. Hardy}, J. Lond. Math. Soc. 20, 48--57 (1945; Zbl 0063.01925); \textit{J. J. Trujillo, M. Rivero} and \textit{B. Bonilla}, J. Math. Anal. 231, No. 1, 255--265 (1999; Zbl 0931.26004); \textit{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.
scientific article; zbMATH DE number 5147005
scientific article