Mellin transforms of generalized fractional integrals and derivatives

Udita N. Katugampola

Applied Mathematics and Computation, 2015, vol. 257, issue C, 566-580

Abstract: We obtain the Mellin transforms of the generalized fractional integrals and derivatives that generalize the Riemann–Liouville and the Hadamard fractional integrals and derivatives. We also obtain interesting results, which combine generalized δr,m operators with generalized Stirling numbers and Lah numbers. For example, we show that δ1,1 corresponds to the Stirling numbers of the 2nd kind and δ2,1 corresponds to the unsigned Lah numbers. Further, we show that the two operators δr,m and δm,r,r,m∈N, generate the same sequence given by the recurrence relation.

Keywords: Generalized fractional derivative; Riemann–Liouville derivative; Hadamard derivative; Mellin transform; Stirling numbers of the 2nd kind; Recurrence relations (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:257:y:2015:i:c:p:566-580

DOI: 10.1016/j.amc.2014.12.067

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