A new definition of fractional derivative

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...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 264; pp. 65 - 70
Main Authors Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2014
Subjects
Fractional derivative
Fractional integral
26A33
Fractional integral
Fractional derivative
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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≤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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2014.01.002