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Mellin transforms of generalized fractional integrals and derivatives

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  • Katugampola, Udita N.

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.

Suggested Citation

  • Katugampola, Udita N., 2015. "Mellin transforms of generalized fractional integrals and derivatives," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 566-580.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:566-580
    DOI: 10.1016/j.amc.2014.12.067
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    Cited by:

    1. Zeng, Shengda & Baleanu, Dumitru & Bai, Yunru & Wu, Guocheng, 2017. "Fractional differential equations of Caputo–Katugampola type and numerical solutions," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 549-554.
    2. Sowa, Marcin, 2018. "Application of SubIval in solving initial value problems with fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 86-103.
    3. Agarwal, Ritu & Kritika, & Purohit, Sunil Dutt, 2021. "Mathematical model pertaining to the effect of buffer over cytosolic calcium concentration distribution," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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