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**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.

### MSC:

26A33 | Fractional derivatives and integrals |

### References:

[1] | Miller, K. S., An Introduction to Fractional Calculus and Fractional Differential Equations (1993), J. Wiley and Sons: J. Wiley and Sons New York · Zbl 0789.26002 |

[2] | Oldham, K.; Spanier, J., The Fractional Calculus, Theory and Applications of Differentiation and Integration of Arbitrary Order (1974), Academic Press: Academic Press USA · Zbl 0292.26011 |

[3] | Kilbas, A.; Srivastava, H.; Trujillo, J., (Theory and Applications of Fractional Differential Equations. Theory and Applications of Fractional Differential Equations, Math. Studies. (2006), North-Holland: North-Holland New York) · Zbl 1092.45003 |

[4] | Podlubny, I., Fractional Differential Equations (1999), Academic Press: Academic Press USA · Zbl 0918.34010 |

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