On the generalized fractional derivatives and their Caputo modification
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Authors
F. Jarad
- Mathematics Department, Faculty of Arts and Sciences, ÇankayaUniversity, 06790, Etimesgut, Ankara, Turkey.
T. Abdeljawad
- Department of Mathematics and Physical Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia.
D. Baleanu
- Mathematics Department, Faculty of Arts and Sciences, ÇankayaUniversity, 06790, Etimesgut, Ankara, Turkey.
- Institute of Space Sciences, Magurele-Bucharest, Romania.
Abstract
In this manuscript, we define the generalized fractional derivative on \(AC^n_\gamma
[a, b]\), the space of functions defined on [a, b]
such that
\(\gamma^{n-1}f\in AC[a, b]\), where
\(\gamma=x^{1-p}\frac{d}{dx}\). We present some of the properties of generalized fractional derivatives of these
functions and then we define their Caputo version.
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ISRP Style
F. Jarad, T. Abdeljawad, D. Baleanu, On the generalized fractional derivatives and their Caputo modification, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 5, 2607--2619
AMA Style
Jarad F., Abdeljawad T., Baleanu D., On the generalized fractional derivatives and their Caputo modification. J. Nonlinear Sci. Appl. (2017); 10(5):2607--2619
Chicago/Turabian Style
Jarad, F., Abdeljawad, T., Baleanu, D.. "On the generalized fractional derivatives and their Caputo modification." Journal of Nonlinear Sciences and Applications, 10, no. 5 (2017): 2607--2619
Keywords
- Riemann-Liouville fractional derivatives
- Caputo fractional derivatives
- Hadamard fractional derivatives
- Caputo-Hadamard fractional derivatives
- generalized fractional integral
- generalized Caputo fractional derivatives.
MSC
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