{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T02:08:27Z","timestamp":1740103707715,"version":"3.37.3"},"reference-count":51,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,7,28]],"date-time":"2020-07-28T00:00:00Z","timestamp":1595894400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007446","name":"King Khalid University","doi-asserted-by":"publisher","award":["R.G.P2.\/99\/41"],"award-info":[{"award-number":["R.G.P2.\/99\/41"]}],"id":[{"id":"10.13039\/501100007446","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,7,28]]},"abstract":"<jats:p>In this paper, the fractional view analysis of the Keller\u2013Segal equations with sensitivity functions is presented. The Caputo operator has been used to pursue the present research work. The natural transform is combined with the homotopy perturbation method, and a new scheme for implementation is derived. The modified established method is named as the homotopy perturbation transform technique. The derived results are compared with the solution of the Laplace Adomian decomposition technique by using the systems of fractional Keller\u2013Segal equations. The solution graphs and the table have shown that the obtained results coincide with the solution of the Laplace Adomian decomposition method. Fractional-order solutions are determined to confirm the reliability of the current method. It is observed that the solutions at various fractional orders are convergent to an integer-order solution of the problems. The suggested procedure is very attractive and straight forward and therefore can be modified to solve high nonlinear fractional partial differential equations and their systems.<\/jats:p>","DOI":"10.1155\/2020\/2371019","type":"journal-article","created":{"date-parts":[[2020,7,28]],"date-time":"2020-07-28T23:33:29Z","timestamp":1595979209000},"page":"1-15","source":"Crossref","is-referenced-by-count":7,"title":["On the Fractional View Analysis of Keller\u2013Segel Equations with Sensitivity Functions"],"prefix":"10.1155","volume":"2020","author":[{"given":"Haobin","family":"Liu","sequence":"first","affiliation":[{"name":"Data Recovery Key Laboratory of Sichuan Province, Neijiang Normal University, Neijiang 641000, Sichuan, China"},{"name":"School of Mathematics and Information Sciences, Neijiang Normal University, Neijiang 641000, Sichuan, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6417-1181","authenticated-orcid":true,"given":"Hassan","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan University Mardan (AWKUM), Mardan, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4306-8489","authenticated-orcid":true,"given":"Rasool","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan University Mardan (AWKUM), Mardan, Pakistan"}]},{"given":"A. 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