A general form of the generalized Taylor’s formula with some applications
作者：
Highlights：
• In this article, a new general form of fractional power series is introduced.
• Some results of classical power series are circulated and proved to this new form.
• A new general form of the generalized Taylor’s formula is also obtained.
• Applications including fractional power series solutions for FDEs are analyzed.
• Results reveal that, the new expansion is effective for formulating the solutions.
摘要
•In this article, a new general form of fractional power series is introduced.•Some results of classical power series are circulated and proved to this new form.•A new general form of the generalized Taylor’s formula is also obtained.•Applications including fractional power series solutions for FDEs are analyzed.•Results reveal that, the new expansion is effective for formulating the solutions.
论文关键词：Fractional differential equations,Caputo fractional derivative,Taylor expansion
论文评审过程：Available online 18 February 2015.
论文官网地址：https://doi.org/10.1016/j.amc.2015.01.034
