Jarad, FahdAbdeljawad, ThabetBaleanu, Dumitru2019-12-182025-09-182019-12-182025-09-182017Jarad, Fahd; Abdeljawad, Thabet; Baleanu, Dumitru (2017). On the generalized fractional derivatives and their Caputo modification, Journal of Nonlinear Sciences And Applications, 10(5), 2607-2619.2008-18982008-1901https://doi.org/10.22436/jnsa.010.05.27https://hdl.handle.net/20.500.12416/12605Abdeljawad, Thabet/0000-0002-8889-3768In this manuscript, we define the generalized fractional derivative on AC(gamma)(n) [a, b], the space of functions defined on [a, b] such that gamma(n-1) f is an element of AC [a, b], where gamma = x(1-rho) d/dx. We present some of the properties of generalized fractional derivatives of these functions and then we define their Caputo version. (C) 2017 All rights reserved.eninfo:eu-repo/semantics/openAccessRiemann-Liouville Fractional DerivativesCaputo Fractional DerivativesHadamard Fractional DerivativesCaputo-Hadamard Fractional DerivativesGeneralized Fractional IntegralGeneralized Caputo Fractional DerivativesArticle10.22436/jnsa.010.05.27