A new definition of fractional derivative

作者:Khalil, R.*; Al Horani, M.; Yousef, A.; Sababheh, M.
来源:Journal of Computational and Applied Mathematics, 2014, 264: 65-70.
DOI:10.1016/j.cam.2014.01.002

摘要

We give a new definition of fractional derivative and fractional integral. The form of the definition shows that it is the most natural definition, and the most fruitful one. The definition for 0 <= alpha < 1 coincides with the classical definitions on polynomials (up to a constant). Further, if alpha = 1, the definition coincides with the classical definition of first derivative. We give some applications to fractional differential equations.

  • 出版日期2014-7