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Riemann–Liouville and Caputo Fractional Potentials Associated with the Number Operator

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Abstract

In order to introduce the Riemann–Liouville (RL) and Caputo (C) fractional potentials, we use the Laplace transform and the Mittag–Leffler function to solve, in infinite dimension, the C time fractional diffusion equation and RL time fractional diffusion equation with respect to the number operator acting on a distribution space. Then, we show that these fractional potentials verify some fractional Poisson equations and some regularity properties.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

The authors would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: (22UQU4350523DSR02). The authors would like to thank the Deanship of Scientific Research at Majmaah University for supporting this work under Project No. RGP-2019-1.

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Authors and Affiliations

  1. Department of Mathematics, College of Science of Al-Zulfi, Majmaah University, P.O. Box 66, Al-Majmaah, 11952, Saudi Arabia

    Ziyad A. Alhussain & Anis Riahi

  2. College of Science, Qassim University, PO. Box 6644, Buraidah, 51452, Saudi Arabia

    Habib Rebei

  3. Department of Mathematics, AL-Qunfudhah University college, Umm Al-Qura University, Mecca, Saudi Arabia

    Hafedh Rguigui

  4. Department of Mathematics, Higher School of Sciences and Technologies of Hammam–Sousse, University of Sousse, Sousse, Tunisia

    Hafedh Rguigui

Authors
  1. Ziyad A. Alhussain
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  2. Habib Rebei
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  3. Hafedh Rguigui
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  4. Anis Riahi
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Correspondence to Hafedh Rguigui.

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Communicated by Daniel Alpay.

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This article is part of the topical collection “Infinite-dimensional Analysis and Non-commutative Theory” edited by Marek Bozejko, Palle Jorgensen and Yuri Kondratiev.

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Alhussain, Z.A., Rebei, H., Rguigui, H. et al. Riemann–Liouville and Caputo Fractional Potentials Associated with the Number Operator. Complex Anal. Oper. Theory 16, 85 (2022). https://doi.org/10.1007/s11785-022-01266-z

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