{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:41:28Z","timestamp":1760186488661,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,1,18]],"date-time":"2019-01-18T00:00:00Z","timestamp":1547769600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Fundamental Research Funds for the Central University","award":["2017XKZD11"],"award-info":[{"award-number":["2017XKZD11"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11371361"],"award-info":[{"award-number":["11371361"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the paper, we discuss some similarity solutions of the time-fractional Burgers system (TFBS). Firstly, with the help of the Lie-point symmetry and the corresponding invariant variables, we transform the TFBS to a fractional ordinary differential system (FODS) under the case where the time-fractional derivative is the Riemann\u2013Liouville type. The FODS can be approximated by some integer-order ordinary differential equations; here, we present three such integer-order ordinary differential equations (called IODE-1, IODE-2, and IODE-3, respectively). For IODE-1, we obtain its similarity solutions and numerical solutions, which approximate the similarity solutions and the numerical solutions of the TFBS. Secondly, we apply the numerical analysis method to obtain the numerical solutions of IODE-2 and IODE-3.<\/jats:p>","DOI":"10.3390\/sym11010112","type":"journal-article","created":{"date-parts":[[2019,1,18]],"date-time":"2019-01-18T11:26:55Z","timestamp":1547810815000},"page":"112","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Some Similarity Solutions and Numerical Solutions to the Time-Fractional Burgers System"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3900-5792","authenticated-orcid":false,"given":"Xiangzhi","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yufeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,18]]},"reference":[{"key":"ref_1","unstructured":"Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. 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