Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel
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Authors
Thabet Abdeljawad
- Department of Mathematics and Physical Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia.
Dumitru Baleanu
- Department of Mathematics, Cankaya University, 06530 Ankara, Turkey.
- Institute of Space Sciences, Magurele-Bucharest, Romania.
Abstract
In this manuscript we define the right fractional derivative and its corresponding right fractional integral for the newly
suggested nonlocal fractional derivative with Mittag-Leffler kernel. Then, we obtain the related integration by parts formula.
We use the Q-operator to confirm our results. The related Euler-Lagrange equations are reported and one illustrative example
is discussed.
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ISRP Style
Thabet Abdeljawad, Dumitru Baleanu, Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 3, 1098--1107
AMA Style
Abdeljawad Thabet, Baleanu Dumitru, Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel. J. Nonlinear Sci. Appl. (2017); 10(3):1098--1107
Chicago/Turabian Style
Abdeljawad, Thabet, Baleanu, Dumitru. "Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel." Journal of Nonlinear Sciences and Applications, 10, no. 3 (2017): 1098--1107
Keywords
- Fractional calculus
- Mittag-Leffler function
- fractional integration by parts
- fractional Euler-Lagrange equations.
MSC
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