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

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.


26A33 Fractional derivatives and integrals
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