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Riemann-Liouville and Caputo Fractional Potentials Associated with the Number Operator
Journal article   Peer reviewed

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

Ziyad A. Alhussain, Habib Rebei, Hafedh Rguigui and Anis Riahi
Complex analysis and operator theory, Vol.16(6)
01/09/2022
DOI: https://doi.org/10.1007/s11785-022-01266-z

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
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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