Romero, Luis Guillermo; Luque, Luciano L.; Dorrego, Gustavo Abel; Cerutti, Rubén A. On the \(k\)-Riemann-Liouville fractional derivative. (English) Zbl 1285.26009 Int. J. Contemp. Math. Sci. 8, No. 1-4, 41-51 (2013). Summary: The main object of this paper is to introduce a new fractional operator called \(k\)-Riemann-Liouville fractional derivative defined by using the \(k\)-gamma function, which is a generalization of the classical gamma function. We also investigate relationships with the \(k\)-Riemann-Liouville integral and derive some properties using Fourier and Laplace transform. Cited in 23 Documents MSC: 26A33 Fractional derivatives and integrals 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type Keywords:\(k\)-fractional calculus; Riemann-Liouville fractional derivative; \(k\)-Riemann-Liouville singular kernel PDFBibTeX XMLCite \textit{L. G. Romero} et al., Int. J. Contemp. Math. Sci. 8, No. 1--4, 41--51 (2013; Zbl 1285.26009) Full Text: DOI Link