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• W3100620871 abstract "Fractional diffusion equations imply non-Gaussian distributions that generalise the standard diffusive process. Recent advances in fractional calculus lead to a class of new fractional operators defined by non-singular memory kernels, differently from the fractional operator defined in the literature. In this work we propose a generalisation of the Fokker-Planck equation in terms of a non-singular fractional temporal operator and considering a non-constant diffusion coefficient. We obtain analytical solutions for the Caputo-Fabrizio and the Atangana-Baleanu fractional kernel operators, from which non-Gaussian distributions emerge having a long and short tails. In addition, we show that these non-Gaussian distributions are unimodal or bimodal according if the diffusion index $nu$ is positive or negative respectively, where a diffusion coefficient of the power law type $mathcal{D}(x)=mathcal{D}_0|x|^{nu}$ is considered. Thereby, a class of anomalous diffusion phenomena connected with fractional derivatives and with a diffusion coefficient of the power law type is presented. The techniques employed in this work open new possibilities for studying memory effects in diffusive contexts." @default.
• W3100620871 created "2020-11-23" @default.
• W3100620871 creator A5011457702 @default.
• W3100620871 creator A5083043154 @default.
• W3100620871 date "2018-12-06" @default.
• W3100620871 modified "2023-09-25" @default.
• W3100620871 title "A fractional Fokker–Planck equation for non-singular kernel operators" @default.
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• W3100620871 doi "https://doi.org/10.1088/1742-5468/aae5a2" @default.
• W3100620871 hasPublicationYear "2018" @default.
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