{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T02:28:34Z","timestamp":1776479314725,"version":"3.51.2"},"reference-count":47,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,4,18]],"date-time":"2023-04-18T00:00:00Z","timestamp":1681776000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Center for Research and Development in Mathematics and Applications (CIDMA)","award":["UIDB\/04106\/2020"],"award-info":[{"award-number":["UIDB\/04106\/2020"]}]},{"name":"Center for Research and Development in Mathematics and Applications (CIDMA)","award":["UIDP\/04106\/2020"],"award-info":[{"award-number":["UIDP\/04106\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>The study of variable order differential equations is important in science and engineering for a better representation and analysis of dynamical problems. In the literature, there are several fractional order operators involving variable orders. In this article, we construct a nonlinear variable order fractional differential system with a p-Laplacian operator. The presumed problem is a general class of the nonlinear equations of variable orders in the ABC sense of derivatives in combination with Caputo\u2019s fractional derivative. We investigate the existence of solutions and the Hyers\u2013Ulam stability of the considered equation. The presumed problem is a hybrid in nature and has a lot of applications. We have given its particular example as a waterborne disease model of variable order which is analysed for the numerical computations for different variable orders. The results obtained for the variable orders have an advantage over the constant orders in that the variable order simulations present the fluctuation of the real dynamics throughout our observations of the simulations.<\/jats:p>","DOI":"10.3390\/math11081913","type":"journal-article","created":{"date-parts":[[2023,4,19]],"date-time":"2023-04-19T01:09:22Z","timestamp":1681866562000},"page":"1913","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["On System of Variable Order Nonlinear p-Laplacian Fractional Differential Equations with Biological Application"],"prefix":"10.3390","volume":"11","author":[{"given":"Hasib","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5262-1138","authenticated-orcid":false,"given":"Jehad","family":"Alzabut","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"},{"name":"Department of Industrial Engineering, OST\u0130M Technical University, Ankara 06374, Turkey"}]},{"given":"Haseena","family":"Gulzar","sequence":"additional","affiliation":[{"name":"Department of Biotechnology, Shaheed Benazir Bhutto University, Sheringal Dir Upper 18000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2965-4561","authenticated-orcid":false,"given":"Osman","family":"Tun\u00e7","sequence":"additional","affiliation":[{"name":"Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University Campus, Van 65080, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0984-0159","authenticated-orcid":false,"given":"Sandra","family":"Pinelas","sequence":"additional","affiliation":[{"name":"Departamento de Ciencias Exatas e Engenharia, Academia Militar, 2720-113 Amadora, Portugal"},{"name":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Deimling, K. 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