A new definition of fractional derivative. (English) Zbl 1297.26013

Khalil, R.; Al Horani, M.; Yousef, A.; Sababheh, M.

J. Comput. Appl. Math. 264, 65-70 (2014).

Summary: 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 \(0\leq {\alpha}<1\) 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.

MSC:

26A33

Fractional derivatives and integrals

Keywords:

fractional derivative; fractional integral

References:

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