{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T23:11:39Z","timestamp":1778627499427,"version":"3.51.4"},"reference-count":66,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T00:00:00Z","timestamp":1740009600000},"content-version":"vor","delay-in-days":50,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>\n                    In science and engineering, nonlinear time\u2010fractional partial differential equations (NTFPDEs) are thought to be a useful tool for describing several natural and physical processes. It is tough to come up with analytical answers for these issues. Finding answers to NTFPDEs is therefore a crucial component of scientific study. To solve nonlinear time\u2010fractional hyperbolic partial differential equations (NTFHPDEs), we provide a novel fractional Shehu transform iterative method (FSTIM) in this work. In this case, the Caputo derivative is used to get the fractional derivative. The method combines two powerful numerical approaches called the fractional Shehu transform and the new iterative method (NIM), also known as the Daftardar\u2010Gejji and Jafari method. Through the recommended scheme, the linear portion of the problem is resolved by employing the Shehu transform method, while the noise terms from the nonlinear portion of the problem disappear over a successive iteration process of the NIM. The solution of FSTIM is then denoted in a series form, which is convergent to the precise answer of the assumed problem. Using principles from Banach\u2019s spaces, the stability and convergence analysis of the suggested approach are addressed. To confirm the effectiveness and accuracy of the method, three illustrations from NTFHPDEs are presented. The obtained results are compared with the exact solutions and the other numerical results existing in the literature in terms of\n                    <jats:italic>L<\/jats:italic>\n                    <jats:sub>\u221e<\/jats:sub>\n                    and\n                    <jats:italic>L<\/jats:italic>\n                    <jats:sub>2<\/jats:sub>\n                    absolute errors. The findings showed that the proposed method outperforms the other numerical techniques in the literature and gives accurate results with a few terms. Therefore, the recommended approach is effective and straightforward and can be applied to other complex nonlinear physical differential equations with fractional order.\n                  <\/jats:p>","DOI":"10.1155\/jama\/7007124","type":"journal-article","created":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T02:10:36Z","timestamp":1740103836000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["An Efficient Numerical Method for Nonlinear Time Fractional Hyperbolic Partial Differential Equations Based on Fractional Shehu Transform Iterative Method"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-5231-8165","authenticated-orcid":false,"given":"Alemu Senbeta","family":"Bekela","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4922-0656","authenticated-orcid":false,"given":"Alemayehu Tamirie","family":"Deresse","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,2,20]]},"reference":[{"key":"e_1_2_11_1_2","volume-title":"Biochemistry","author":"Voet D.","year":"2011"},{"key":"e_1_2_11_2_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-024-54870-8"},{"key":"e_1_2_11_3_2","doi-asserted-by":"publisher","DOI":"10.3390\/fractalfract8060363"},{"key":"e_1_2_11_4_2","doi-asserted-by":"publisher","DOI":"10.3390\/fractalfract8070369"},{"key":"e_1_2_11_5_2","doi-asserted-by":"publisher","DOI":"10.1155\/2024\/9955247"},{"key":"e_1_2_11_6_2","doi-asserted-by":"publisher","DOI":"10.1515\/tmj-2017-0010"},{"key":"e_1_2_11_7_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218348X24500828"},{"key":"e_1_2_11_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12346-024-01004-0"},{"key":"e_1_2_11_9_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13104-024-06877-7"},{"key":"e_1_2_11_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.padiff.2024.100948"},{"key":"e_1_2_11_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40815-023-01569-z"},{"key":"e_1_2_11_12_2","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/535793"},{"key":"e_1_2_11_13_2","doi-asserted-by":"publisher","DOI":"10.3390\/fractalfract6010032"},{"key":"e_1_2_11_14_2","doi-asserted-by":"publisher","DOI":"10.1108\/EC-01-2019-0011"},{"key":"e_1_2_11_15_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0302743"},{"key":"e_1_2_11_16_2","doi-asserted-by":"publisher","DOI":"10.1177\/16878132241241435"},{"key":"e_1_2_11_17_2","doi-asserted-by":"publisher","DOI":"10.1002\/cey2.360"},{"key":"e_1_2_11_18_2","doi-asserted-by":"publisher","DOI":"10.1155\/2023\/4664866"},{"key":"e_1_2_11_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.padiff.2024.100950"},{"key":"e_1_2_11_20_2","doi-asserted-by":"publisher","DOI":"10.3389\/fphy.2023.1168795"},{"key":"e_1_2_11_21_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-020-03048-3"},{"key":"e_1_2_11_22_2","doi-asserted-by":"publisher","DOI":"10.32792\/jeps.v14i2.429"},{"key":"e_1_2_11_23_2","doi-asserted-by":"publisher","DOI":"10.17485\/IJST\/v17i41.2982"},{"key":"e_1_2_11_24_2","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2024.3405791"},{"key":"e_1_2_11_25_2","first-page":"25","article-title":"Solving high-order nonlinear partial differential equations by modified q-homotopy analysis method","volume":"4","author":"Huseen S. N.","year":"2020","journal-title":"Asian Journal of Mathematical Sciences"},{"key":"e_1_2_11_26_2","doi-asserted-by":"publisher","DOI":"10.1155\/2022\/7192231"},{"key":"e_1_2_11_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.padiff.2023.100540"},{"key":"e_1_2_11_28_2","doi-asserted-by":"publisher","DOI":"10.18576\/pfda\/070107"},{"key":"e_1_2_11_29_2","article-title":"A new approach to find approximate solutions of Burger\u2019s and coupled Burger\u2019s equations of fractional order","volume":"11","author":"Jassim H. K.","year":"2021","journal-title":"TWMS Journal of Applied and Engineering Mathematics"},{"key":"e_1_2_11_30_2","doi-asserted-by":"publisher","DOI":"10.48048\/tis.2023.4410"},{"key":"e_1_2_11_31_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13661-024-01851-5"},{"key":"e_1_2_11_32_2","doi-asserted-by":"publisher","DOI":"10.1155\/2022\/6977692"},{"key":"e_1_2_11_33_2","doi-asserted-by":"publisher","DOI":"10.1155\/2022\/2466367"},{"key":"e_1_2_11_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mex.2024.102865"},{"key":"e_1_2_11_35_2","doi-asserted-by":"publisher","DOI":"10.3390\/math12132145"},{"key":"e_1_2_11_36_2","doi-asserted-by":"publisher","DOI":"10.1155\/2024\/5541845"},{"key":"e_1_2_11_37_2","doi-asserted-by":"publisher","DOI":"10.2478\/amns.2023.1.00110"},{"key":"e_1_2_11_38_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-15-0098-5_4"},{"key":"e_1_2_11_39_2","first-page":"64","article-title":"Convergence of Riemann-Liouvelli and Caputo derivative definitions for practical solution of fractional order differential equation","volume":"23","author":"Das S.","year":"2011","journal-title":"International Journal of Applied Mathematics and Statistics"},{"key":"e_1_2_11_40_2","first-page":"529","article-title":"Sequential Caputo versus nonsequential Caputo fractional initial and boundary value problems","volume":"15","author":"Vatsala A. S.","year":"2020","journal-title":"International Journal of Differential Equations"},{"key":"e_1_2_11_41_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.08.036"},{"key":"e_1_2_11_42_2","doi-asserted-by":"publisher","DOI":"10.1080\/25765299.2019.1706234"},{"key":"e_1_2_11_43_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.6484"},{"key":"e_1_2_11_44_2","doi-asserted-by":"publisher","DOI":"10.3390\/math9020141"},{"key":"e_1_2_11_45_2","doi-asserted-by":"publisher","DOI":"10.3390\/math10121961"},{"key":"e_1_2_11_46_2","doi-asserted-by":"publisher","DOI":"10.1515\/nleng-2022-0024"},{"key":"e_1_2_11_47_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.padiff.2024.100890"},{"key":"e_1_2_11_48_2","doi-asserted-by":"publisher","DOI":"10.37256\/cm.5120243192"},{"key":"e_1_2_11_49_2","doi-asserted-by":"publisher","DOI":"10.22034\/cmde.2024.61746.2683"},{"key":"e_1_2_11_50_2","doi-asserted-by":"publisher","DOI":"10.15446\/recolma.v56n1.105612"},{"key":"e_1_2_11_51_2","doi-asserted-by":"publisher","DOI":"10.1080\/10407790.2020.1803602"},{"key":"e_1_2_11_52_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.5590"},{"key":"e_1_2_11_53_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.rico.2023.100307"},{"key":"e_1_2_11_54_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.5375"},{"key":"e_1_2_11_55_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0219876217500293"},{"key":"e_1_2_11_56_2","first-page":"167","article-title":"New integral transform: Shehu transform a generalization of Sumudu and Laplace transform for solving differential equations","volume":"17","author":"Maitama S.","year":"2019","journal-title":"International Journal of Analysis and Applications"},{"key":"e_1_2_11_57_2","doi-asserted-by":"publisher","DOI":"10.3390\/app10010122"},{"key":"e_1_2_11_58_2","first-page":"26","article-title":"Primitive of second kind linear Volterra integral equation using Shehu transform","volume":"9","author":"Aggarwal S.","year":"2020","journal-title":"International Journal of Latest Technology in Engineering, Management & Applied Science"},{"key":"e_1_2_11_59_2","first-page":"917","article-title":"Shehu transform and applications to Caputo-fractional differential equations","volume":"17","author":"Belgacem R.","year":"2019","journal-title":"International Journal of Analysis and Applications"},{"key":"e_1_2_11_60_2","doi-asserted-by":"publisher","DOI":"10.1007\/s13398-024-01636-6"},{"key":"e_1_2_11_61_2","doi-asserted-by":"publisher","DOI":"10.58715\/ncao.2024.3.3"},{"key":"e_1_2_11_62_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.joes.2021.12.002"},{"key":"e_1_2_11_63_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.padiff.2024.100744"},{"key":"e_1_2_11_64_2","doi-asserted-by":"publisher","DOI":"10.1115\/1.4032767"},{"key":"e_1_2_11_65_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2006.10.025"},{"key":"e_1_2_11_66_2","first-page":"91","article-title":"Applications of homotopy perturbation method and Elzaki transform for solving nonlinear partial differential equations of fractional order","volume":"2015","author":"Neamaty A.","year":"2016","journal-title":"Journal of Nonlinear Evolution Equations and Applications"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/7007124","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/jama\/7007124","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/7007124","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T02:42:27Z","timestamp":1776393747000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/jama\/7007124"}},"subtitle":[],"editor":[{"given":"Kannan","family":"Krithivasan","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":66,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10.1155\/jama\/7007124"],"URL":"https:\/\/doi.org\/10.1155\/jama\/7007124","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1]]},"assertion":[{"value":"2024-08-06","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-01-29","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-02-20","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"7007124"}}