{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,12]],"date-time":"2026-07-12T05:31:55Z","timestamp":1783834315850,"version":"3.55.0"},"reference-count":49,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,19]],"date-time":"2024-02-19T00:00:00Z","timestamp":1708300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of  Scientific Research at Imam Mohammad Ibn Saud Islamic  University (IMSIU)","award":["IMSIU-RP23066"],"award-info":[{"award-number":["IMSIU-RP23066"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this study, we present the generalized form of the higher-order nonlinear fractional Bratu-type equation. In this generalization, we deal with a generalized fractional derivative, which is quite useful from an application point of view. Furthermore, some special cases of the generalized fractional Bratu equation are recognized and examined. To solve these nonlinear differential equations of fractional order, we employ the homotopy perturbation transform method. This work presents a useful computational method for solving these equations and advances our understanding of them. We also plot some numerical outcomes to show the efficiency of the obtained results.<\/jats:p>","DOI":"10.3390\/axioms13020133","type":"journal-article","created":{"date-parts":[[2024,2,19]],"date-time":"2024-02-19T10:40:15Z","timestamp":1708339215000},"page":"133","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Analytical Solution of Generalized Bratu-Type Fractional Differential Equations Using the Homotopy Perturbation Transform Method"],"prefix":"10.3390","volume":"13","author":[{"given":"Ghaliah","family":"Alhamzi","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11989, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aafrin","family":"Gouri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Amity School of Applied Sciences, Amity University Rajasthan, Jaipur 302002, Rajasthan, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Badr Saad T.","family":"Alkahtani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, Riyadh 11989, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ravi Shanker","family":"Dubey","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Amity School of Applied Sciences, Amity University Rajasthan, Jaipur 302002, Rajasthan, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,19]]},"reference":[{"key":"ref_1","unstructured":"Miller, K.S., and Ross, B. 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