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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| Published in | Journal of computational and applied mathematics Vol. 264; pp. 65 - 70 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.07.2014
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| Subjects | |
| Online Access | Get full text |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Yousef, A. Khalil, R. Sababheh, M. Al Horani, M. |
| Author_xml | – sequence: 1 givenname: R. surname: Khalil fullname: Khalil, R. email: roshdi@ju.edu.jo organization: Department of Mathematics, The University of Jordan, Al Jubaiha, Amman 11942, Jordan – sequence: 2 givenname: M. surname: Al Horani fullname: Al Horani, M. email: horani@ju.edu.jo organization: Department of Mathematics, The University of Jordan, Al Jubaiha, Amman 11942, Jordan – sequence: 3 givenname: A. surname: Yousef fullname: Yousef, A. email: abd.yousef@ju.edu.jo organization: Department of Mathematics, The University of Jordan, Al Jubaiha, Amman 11942, Jordan – sequence: 4 givenname: M. surname: Sababheh fullname: Sababheh, M. email: sababheh@psut.edu.jo, msababheh@sharjah.ac.ae organization: Department of Basic Sciences, Princess Sumaya University For Technology, Al Jubaiha, Amman 11941, Jordan |
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| References | Kilbas, Srivastava, Trujillo (br000015) 2006 Oldham, Spanier (br000010) 1974 Podlubny (br000020) 1999 Miller (br000005) 1993 Oldham (10.1016/j.cam.2014.01.002_br000010) 1974 Podlubny (10.1016/j.cam.2014.01.002_br000020) 1999 Miller (10.1016/j.cam.2014.01.002_br000005) 1993 Kilbas (10.1016/j.cam.2014.01.002_br000015) 2006 |
| References_xml | – year: 1999 ident: br000020 article-title: Fractional Differential Equations – year: 2006 ident: br000015 publication-title: Theory and Applications of Fractional Differential Equations – year: 1974 ident: br000010 article-title: The Fractional Calculus, Theory and Applications of Differentiation and Integration of Arbitrary Order – year: 1993 ident: br000005 article-title: An Introduction to Fractional Calculus and Fractional Differential Equations – year: 1999 ident: 10.1016/j.cam.2014.01.002_br000020 – year: 2006 ident: 10.1016/j.cam.2014.01.002_br000015 – year: 1993 ident: 10.1016/j.cam.2014.01.002_br000005 – year: 1974 ident: 10.1016/j.cam.2014.01.002_br000010 |
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| Snippet | 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... |
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| SubjectTerms | Fractional derivative Fractional integral |
| Title | A new definition of fractional derivative |
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