# On the generalized fractional derivatives and their Caputo modification

Volume 10, Issue 5, pp 2607--2619 Publication Date: May 25, 2017       Article History
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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.

### Keywords

• Riemann-Liouville fractional derivatives
• Caputo fractional derivatives
• generalized fractional integral
• generalized Caputo fractional derivatives.

•  26A33
•  34A08

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