On the generalized fractional derivatives and their Caputo modification


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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