A new definition of fractional derivative

• Published in: Journal of computational and applied mathematics Vol. 264; pp. 65 - 70
• Main Authors: Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2014
• Subjects: Fractional derivative; Fractional integral; 26A33; Fractional integral; 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...