International audienceWe present perturbative analytical results of the Landau level quasienergy spectrum, autocorrelation function, and out-of-plane pseudospin polarization for a single graphene sheet subject to intense circularly polarized Terahertz radiation. For the quasienergy spectrum, we find a striking nontrivial level-dependent dynamically induced gap structure. This photoinduced modulation of the energy band structure gives rise to shifts of the revival times in the autocorrelation function and it also leads to modulation of the oscillations in the dynamical evolution of the out-of-plane pseudospin polarization, which measures the angular momentum transfer between light and graphene electrons. For a coherent state, chosen as an initial pseudospin configuration, the dynamics induces additional quantum revivals of the wave function that manifest as shifts of the maxima and minima of the autocorrelation function, with additional partial revivals and beating patterns. These additional maxima and beating patterns stem from the effective dynamical coupling of the static eigenstates. We discuss the possible experimental detection schemes of our theoretical results and their relevance in new practical implementation of radiation fields in graphene physics

In this work, we construct a modified version of the Einstein field equations for a vacuum and spherically symmetric spacetime in terms of the Riemann–Liouville fractional derivative. The main difference between our approach and other works is that we ensure that both the classical differential equations and the classical solutions are exactly recovered in the limit when the fractional parameter is turned off. We assume that the fractional equations are valid inside and near the horizon radius and match the classical solution at the horizon. Our approach resembles the Herrera–Witten strategy (Adv High Energy Phys 2018:3839103, 2018, https://doi.org/10.1155/2018/3839103, arXiv:1806.07143 [gr-qc]), where the authors constructed an alternative black hole solution by assuming that inside the horizon the spacetime is hyperbolically symmetric and matches the classical spherically symmetric exterior solution at one point at the horizon. We obtain that, depending on the value of the fractional parameter, the solutions can be interpreted as a regular black hole or a gravastar. As a final step, we compute the fractional curvature scalars and show that the solution is regular everywhere inside the horizon.

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In this paper, we present a characterization of all linear fractional order partial differential operators with complex-valued coefficients that are associated to the generalized fractional Cauchy-Riemann operator in the Riemann-Liouville sense. To achieve our goal, we make use of the technique of an associated differential operator applied to the fractional case.

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