{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:46:48Z","timestamp":1760147208732,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,17]],"date-time":"2023-01-17T00:00:00Z","timestamp":1673913600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research of Imam Mohammad Ibn Saud Islamic University (IMSIU)","award":["RP-21-09-06"],"award-info":[{"award-number":["RP-21-09-06"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The integral-order derivative is not suitable where infinite variances are expected, and the fractional derivative manages to consider effects with more precision; therefore, we considered timefractional Emden\u2013Fowler-type equations and solved them using the rational homotopy perturbation method (RHPM). The RHPM method is based on two power series in rational form. The existence and uniqueness of the equation are proved using the Banach fixed-point theorem. Furthermore, we approximate the term h(z) with a polynomial of a suitable degree and then solve the system using the proposed method and obtain an approximate symmetric solution. Two numerical examples are investigated using this proposed approach. The effectiveness of the proposed approach is checked by representing the graphs of exact and approximate solutions. The table of absolute error is also presented to understand the method\u2032s accuracy.<\/jats:p>","DOI":"10.3390\/sym15020258","type":"journal-article","created":{"date-parts":[[2023,1,17]],"date-time":"2023-01-17T04:28:47Z","timestamp":1673929727000},"page":"258","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Numerical Solution of Time-Fractional Emden\u2013Fowler-Type Equations Using the Rational Homotopy Perturbation Method"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1204-8568","authenticated-orcid":false,"given":"Kholoud Saad","family":"Albalawi","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University, Riyadh 11566, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2864-6888","authenticated-orcid":false,"given":"Badr Saad","family":"Alkahtani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, Riyadh 11989, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ashish","family":"Kumar","sequence":"additional","affiliation":[{"name":"School of Liberal Studies, Dr B.R. Ambedkar University Delhi, Delhi 110006, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1205-1975","authenticated-orcid":false,"given":"Pranay","family":"Goswami","sequence":"additional","affiliation":[{"name":"School of Liberal Studies, Dr B.R. Ambedkar University Delhi, Delhi 110006, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"57","DOI":"10.2475\/ajs.s2-50.148.57","article-title":"On the theoretical temperature of the Sun under the hypothesis of a gaseous mass maintaining its volume by its internal heat and depending on the laws of gases known to terrestrial experiment","volume":"50","author":"Lane","year":"1870","journal-title":"Am. J. Sci."},{"key":"ref_2","unstructured":"Emden, R. (1907). 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