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On the \(k\)-Riemann-Liouville fractional derivative. (English) Zbl 1285.26009

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.

MSC:

26A33 Fractional derivatives and integrals
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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