A new definition of fractional derivative - Khalil, R.; Al Horani, M.; Yousef, A.; Sababheh, M. (Journal of computational and applied mathematics, 2014)
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≤α<1 coincides with the classical definitions on polynomials (up to a constant). Further, if α=1, the definition coincides with the classical definition of first derivative. We give some applications to fractional differential equations.