{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T21:13:18Z","timestamp":1771535598911,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T00:00:00Z","timestamp":1672272000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Spanish Government","award":["RTI2018-094336-B-I00"],"award-info":[{"award-number":["RTI2018-094336-B-I00"]}]},{"name":"Spanish Government","award":["IT1207-19"],"award-info":[{"award-number":["IT1207-19"]}]},{"name":"Spanish Government","award":["IT1555-22"],"award-info":[{"award-number":["IT1555-22"]}]},{"name":"Basque Government","award":["RTI2018-094336-B-I00"],"award-info":[{"award-number":["RTI2018-094336-B-I00"]}]},{"name":"Basque Government","award":["IT1207-19"],"award-info":[{"award-number":["IT1207-19"]}]},{"name":"Basque Government","award":["IT1555-22"],"award-info":[{"award-number":["IT1555-22"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Drugs have always been one of the most important concerns of families and government officials at all times, and they have caused irreparable damage to the health of young people. Given the importance of this great challenge, this article discusses a non-symmetric fractal-fractional order ice-smoking mathematical model for the existence results, numerical results, and stability analysis. For the existence of the solution of the given ice-smoking model, successive iterative sequences are defined. The uniqueness of the solution Hyers\u2013Ulam (HU) stability is established with the help of the existing definitions and theorems in functional analysis. By the utilization of two-step Lagrange polynomials, we provide numerical solutions and provide a comparative numerical analysis for different values of the fractional order and fractal order. The numerical simulations show the applicability of the scheme and future prediction and the effects of fractal-fractional orders simultaneously.<\/jats:p>","DOI":"10.3390\/sym15010087","type":"journal-article","created":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T02:59:01Z","timestamp":1672282741000},"page":"87","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["On Non-Symmetric Fractal-Fractional Modeling for Ice Smoking: Mathematical Analysis of Solutions"],"prefix":"10.3390","volume":"15","author":[{"given":"Anwar","family":"Shah","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Malakand, Dir Lower, Chakdara 18800, Khyber Pakhtunkhwa, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7186-8435","authenticated-orcid":false,"given":"Hasib","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"},{"name":"Department of Mathematics, Shaheed Benazir Bhutto University, Dir Upper, Sheringal 18050, Khyber Pakhtunkhwa, Pakistan"}]},{"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 (UPV\/EHU), 48940 Leioa, Bizkaia, Spain"}]},{"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, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1574-1800","authenticated-orcid":false,"given":"Sina","family":"Etemad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7990-9430","authenticated-orcid":false,"given":"Chernet Tuge","family":"Deressa","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Natural Sciences, Jimma University, Jimma P.O. Box 378, Ethiopia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3463-2607","authenticated-orcid":false,"given":"Shahram","family":"Rezapour","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,29]]},"reference":[{"key":"ref_1","unstructured":"McCoy, A. (1972). The Politics of Heroin in Southeast Asia, Harper and Row."},{"key":"ref_2","unstructured":"Cady, J.F. (1958). A History of Modern Burma, Cornell University Press."},{"key":"ref_3","unstructured":"Khan, N., and Fahad, S. (2022, December 06). Review of Ice Drugs Utilization in Pakistan. 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