{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T20:29:07Z","timestamp":1762374547588,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,7]],"date-time":"2024-09-07T00:00:00Z","timestamp":1725667200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Jilin Provincial Natural Science Foundation of China","award":["YDZJ202201ZYTS535","JJKH20220151KJ"],"award-info":[{"award-number":["YDZJ202201ZYTS535","JJKH20220151KJ"]}]},{"name":"Project of Education Department of Jilin Province of China","award":["YDZJ202201ZYTS535","JJKH20220151KJ"],"award-info":[{"award-number":["YDZJ202201ZYTS535","JJKH20220151KJ"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The space fractional advection\u2013diffusion equation is a crucial type of fractional partial differential equation, widely used for its ability to more accurately describe natural phenomena. Due to the complexity of analytical approaches, this paper focuses on its numerical investigation. A lattice Boltzmann model for the spatial fractional convection\u2013diffusion equation is developed, and an error analysis is carried out. The spatial fractional convection\u2013diffusion equation is solved for several examples. The validity of the model is confirmed by comparing its numerical solutions with those obtained from other methods The results demonstrate that the lattice Boltzmann method is an effective tool for solving the space fractional convection\u2013diffusion equation.<\/jats:p>","DOI":"10.3390\/e26090768","type":"journal-article","created":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T05:06:06Z","timestamp":1725858366000},"page":"768","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Lattice Boltzmann Simulation of Spatial Fractional Convection\u2013Diffusion Equation"],"prefix":"10.3390","volume":"26","author":[{"given":"Xiaohua","family":"Bi","sequence":"first","affiliation":[{"name":"School of Liberal Arts and Sciences, North China Institute of Aerospace Engineering, Langfang 065000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9832-4876","authenticated-orcid":false,"given":"Huimin","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1016\/j.chaos.2019.04.020","article-title":"Modeling attractors of chaotic dynamical systems with fractal-fractional operators","volume":"123","author":"Atangana","year":"2019","journal-title":"Chaos Solitons Fractals"},{"key":"ref_2","first-page":"937","article-title":"A fractional model for the dynamics of tuberculosis (TB) using Atangana-Baleanu derivative","volume":"13","author":"Ullah","year":"2020","journal-title":"Discret. 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