{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:39:01Z","timestamp":1760150341804,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,16]],"date-time":"2023-11-16T00:00:00Z","timestamp":1700092800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002383","name":"Researchers Supporting Project, King Saud University","doi-asserted-by":"publisher","award":["RSP2023R210"],"award-info":[{"award-number":["RSP2023R210"]}],"id":[{"id":"10.13039\/501100002383","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>To solve the fractional gas dynamic equation, this paper presents an effective algorithm using the collocation method and M\u00fcntz-Legendre (M-L) polynomials. The approach chooses a solution of a finite-dimensional space that satisfies the desired equation at a set of collocation points. The collocation points in this study are selected to be uniformly spaced meshes or the roots of shifted Legendre and Chebyshev polynomials. M\u00fcntz-Legendre polynomials have the interesting property that their fractional derivative is also a M\u00fcntz-Legendre polynomial. This property ensures that these bases do not face the problems associated with using the classical orthogonal polynomials when solving fractional equations using the collocation method. The numerical simulations illustrate the method\u2019s effectiveness and accuracy.<\/jats:p>","DOI":"10.3390\/sym15112076","type":"journal-article","created":{"date-parts":[[2023,11,16]],"date-time":"2023-11-16T07:11:27Z","timestamp":1700118687000},"page":"2076","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Solving Fractional Gas Dynamics Equation Using M\u00fcntz\u2013Legendre Polynomials"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9394-7305","authenticated-orcid":false,"given":"Haifa","family":"Bin Jebreen","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7504-0424","authenticated-orcid":false,"given":"Carlo","family":"Cattani","sequence":"additional","affiliation":[{"name":"Engineering School (DEIM), University of Tuscia, Largo dell\u2019Universit\u00e0, 01100 Viterbo, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,16]]},"reference":[{"key":"ref_1","first-page":"215856","article-title":"Fractional Differential Equations","volume":"2010","author":"Liu","year":"2010","journal-title":"Int. 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