Modeling Anomalous Transport of Cosmic Rays in the Heliosphere Using a Fractional Fokker–Planck Equation
Cosmic rays exhibit anomalous diffusion behaviors in the heliospheric environment that cannot be adequately described by classical diffusion models. In this paper, we develop a theoretical framework employing a fractional Fokker–Planck equation to model the anomalous transport of cosmic rays. This a...
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2025-01-01
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| author | José Luis Díaz Palencia |
| author_facet | José Luis Díaz Palencia |
| author_sort | José Luis Díaz Palencia |
| collection | DOAJ |
| description | Cosmic rays exhibit anomalous diffusion behaviors in the heliospheric environment that cannot be adequately described by classical diffusion models. In this paper, we develop a theoretical framework employing a fractional Fokker–Planck equation to model the anomalous transport of cosmic rays. This approach accounts for the observed non-Gaussian distributions, long-range correlations and memory effects in cosmic ray fluxes. We derive analytical solutions using the Adomian Decomposition Method and express them in terms of Mittag-Leffler functions and Lévy stable distributions. The model parameters, including the fractional orders <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> and the entropic index <i>q</i>, are estimated by a short comparison between theoretical predictions and observational data from cosmic ray experiments. Our findings suggest that the integration of fractional calculus and non-extensive statistics can be employed for describing the cosmic ray propagation and the anomalous diffusion observed in the heliosphere. |
| format | Article |
| id | doaj-art-0129e1cf13fa4672871974fb3fac198d |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-01-01 |
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| series | Fractal and Fractional |
| spelling | doaj-art-0129e1cf13fa4672871974fb3fac198d2025-01-24T13:33:24ZengMDPI AGFractal and Fractional2504-31102025-01-01912410.3390/fractalfract9010024Modeling Anomalous Transport of Cosmic Rays in the Heliosphere Using a Fractional Fokker–Planck EquationJosé Luis Díaz Palencia0Department of Mathematics and Education, Universidad a Distancia de Madrid, 28400 Madrid, SpainCosmic rays exhibit anomalous diffusion behaviors in the heliospheric environment that cannot be adequately described by classical diffusion models. In this paper, we develop a theoretical framework employing a fractional Fokker–Planck equation to model the anomalous transport of cosmic rays. This approach accounts for the observed non-Gaussian distributions, long-range correlations and memory effects in cosmic ray fluxes. We derive analytical solutions using the Adomian Decomposition Method and express them in terms of Mittag-Leffler functions and Lévy stable distributions. The model parameters, including the fractional orders <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> and the entropic index <i>q</i>, are estimated by a short comparison between theoretical predictions and observational data from cosmic ray experiments. Our findings suggest that the integration of fractional calculus and non-extensive statistics can be employed for describing the cosmic ray propagation and the anomalous diffusion observed in the heliosphere.https://www.mdpi.com/2504-3110/9/1/24cosmic raysanomalous diffusionfractional calculusTsallis statistics |
| spellingShingle | José Luis Díaz Palencia Modeling Anomalous Transport of Cosmic Rays in the Heliosphere Using a Fractional Fokker–Planck Equation Fractal and Fractional cosmic rays anomalous diffusion fractional calculus Tsallis statistics |
| title | Modeling Anomalous Transport of Cosmic Rays in the Heliosphere Using a Fractional Fokker–Planck Equation |
| title_full | Modeling Anomalous Transport of Cosmic Rays in the Heliosphere Using a Fractional Fokker–Planck Equation |
| title_fullStr | Modeling Anomalous Transport of Cosmic Rays in the Heliosphere Using a Fractional Fokker–Planck Equation |
| title_full_unstemmed | Modeling Anomalous Transport of Cosmic Rays in the Heliosphere Using a Fractional Fokker–Planck Equation |
| title_short | Modeling Anomalous Transport of Cosmic Rays in the Heliosphere Using a Fractional Fokker–Planck Equation |
| title_sort | modeling anomalous transport of cosmic rays in the heliosphere using a fractional fokker planck equation |
| topic | cosmic rays anomalous diffusion fractional calculus Tsallis statistics |
| url | https://www.mdpi.com/2504-3110/9/1/24 |
| work_keys_str_mv | AT joseluisdiazpalencia modelinganomaloustransportofcosmicraysintheheliosphereusingafractionalfokkerplanckequation |