{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T19:18:51Z","timestamp":1773515931461,"version":"3.50.1"},"reference-count":26,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,6]],"date-time":"2023-03-06T00:00:00Z","timestamp":1678060800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Basque Government","award":["IT1555-22"],"award-info":[{"award-number":["IT1555-22"]}]},{"name":"Basque Government","award":["KK-2022\/00090 MCIN\/AEI 269.10.13039\/501100011033\/FEDER,UE"],"award-info":[{"award-number":["KK-2022\/00090 MCIN\/AEI 269.10.13039\/501100011033\/FEDER,UE"]}]},{"name":"Basque Government","award":["PID2021-1235430B-C21 MCIN\/AEI 269.10.13039\/501100011033\/FEDER,UE"],"award-info":[{"award-number":["PID2021-1235430B-C21 MCIN\/AEI 269.10.13039\/501100011033\/FEDER,UE"]}]},{"name":"Basque Government","award":["PID2021-1235430B-C22"],"award-info":[{"award-number":["PID2021-1235430B-C22"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study presents a mathematical model of non-integer order through the fractal fractional Caputo operator to determine the development of Ebola virus infections. To construct the model and conduct analysis, all Ebola virus cases are taken as incidence data. A symmetric approach is utilized for qualitative and quantitative analysis of the fractional order model. Additionally, stability is evaluated, along with the local and global effects of the virus that causes Ebola. Using the fractional order model of Ebola virus infections, the existence and uniqueness of solutions, as well the posedness and biological viability and disease free equilibrium points are confirmed. Many applications of fractional operators in modern mathematics exist, including the intricate and important study of symmetrical systems. Symmetry analysis is a powerful tool that enables the creation of numerical solutions for a given fractional differential equation very methodically. For this, we compare the results with the Caputo derivative operator to understand the dynamic behavior of the disease. The simulation demonstrates how all classes have convergent characteristics and maintain their places over time, reflecting the true behavior of Ebola virus infection. Power law kernel with the two step polynomial Newton method were used. This model seems to be quite strong and capable of reproducing the issue\u2019s anticipated theoretical conditions.<\/jats:p>","DOI":"10.3390\/sym15030665","type":"journal-article","created":{"date-parts":[[2023,3,7]],"date-time":"2023-03-07T02:30:45Z","timestamp":1678156245000},"page":"665","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Epidemiological Analysis of Symmetry in Transmission of the Ebola Virus with Power Law Kernel"],"prefix":"10.3390","volume":"15","author":[{"given":"Ali","family":"Hasan","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, The University of Lahore, Lahore 54590, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9832-1424","authenticated-orcid":false,"given":"Ali","family":"Akg\u00fcl","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Mathematics, Lebanese American University, Beirut 5053, Lebanon"},{"name":"Faculty of Arts and Sciences, Department of Mathematics, Near East University, Lefko\u015fa 99138, Turkey"},{"name":"Art and Science Faculty, Department of Mathematics, Siirt University, Siirt 56100, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7616-0500","authenticated-orcid":false,"given":"Muhammad","family":"Farman","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Mathematics, Lebanese American University, Beirut 5053, Lebanon"},{"name":"Faculty of Arts and Sciences, Department of Mathematics, Near East University, Lefko\u015fa 99138, Turkey"},{"name":"Institute of Mathematics, Khawaja Fareed University of Engineering and Information Technology, Rahim Yar Khan 64200, Pakistan"}]},{"given":"Faryal","family":"Chaudhry","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, The University of Lahore, Lahore 54590, Pakistan"}]},{"given":"Muhammad","family":"Sultan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sait University, Calgary, AB 56000, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9320-9433","authenticated-orcid":false,"given":"Manuel","family":"De la Sen","sequence":"additional","affiliation":[{"name":"Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country, 48940 Leioa, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1146\/annurev-pathol-052016-100506","article-title":"The pathogenesis of Ebola virus disease","volume":"12","author":"Baseler","year":"2017","journal-title":"Ann. 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