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Fractional Number Operator and Associated Fractional Diffusion Equations

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Abstract

In this paper, we study the fractional number operator as an analog of the finite-dimensional fractional Laplacian. An important relation with the Ornstein-Uhlenbeck process is given. Using a semigroup approach, the solution of the Cauchy problem associated to the fractional number operator is presented. By means of the Mittag-Leffler function and the Laplace transform, we give the solution of the Caputo time fractional diffusion equation and Riemann-Liouville time fractional diffusion equation in infinite dimensions associated to the fractional number operator.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El-Manar, 1060, Tunis, Tunisia

    Hafedh Rguigui

  2. Department of Mathematics, AL-Qunfudhah University College, Umm Al-Qura University, Mecca, Saudi Arabia

    Hafedh Rguigui

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  1. Hafedh Rguigui
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Correspondence to Hafedh Rguigui.

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Rguigui, H. Fractional Number Operator and Associated Fractional Diffusion Equations. Math Phys Anal Geom 21, 1 (2018). https://doi.org/10.1007/s11040-017-9261-1

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  • DOI: https://doi.org/10.1007/s11040-017-9261-1

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