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The derivative of fractional order is represented in the Atangana\u2013Baleanu derivative. The numerical examples are combined for their approximate\u2010analytical solution. It is explored using graphs that indicate that the actual and approximation results are close to each other, demonstrating the method\u2019s usefulness. Fractional\u2010order solutions are the most in line with the dynamics of the targeted problems, and they provide an endless number of options for an optimal mathematical model solution for a particular physical phenomenon. This analytical approach produces a series form solution that is quickly convergent to exact solutions. The acquired results suggest that the novel analytical solution technique is simple to use and very successful at assessing complicated problems that arise in related fields of research and technology.<\/jats:p>","DOI":"10.1155\/2022\/7635696","type":"journal-article","created":{"date-parts":[[2022,9,24]],"date-time":"2022-09-24T12:35:08Z","timestamp":1664022908000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Analytical Investigation of Some Dynamical Systems by ZZ Transform with Mittag\u2013Leffler Kernel"],"prefix":"10.1155","volume":"2022","author":[{"given":"Mounirah","family":"Areshi","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4755-9381","authenticated-orcid":false,"given":"Muhammad","family":"Naeem","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8425-6446","authenticated-orcid":false,"given":"Noorolhuda","family":"Wyal","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2022,9,24]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.61.132"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1142\/p614"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2006.05.030"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.66.060102"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2010.08.003"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-01411-1"},{"key":"e_1_2_9_7_2","volume-title":"An Introduction to the Fractional Calculus and Fractional Differential Equations","author":"Miller K. 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