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The fractional model is further reformulated via a generalized fractal-fractional differential operator in the Caputo sense. The basic mathematical including the existence and uniqueness of both fractional and fractal-fractional problems are provided using fixed points theorems. A numerical scheme for the proposed model is obtained using an efficient iterative method. Moreover, detailed simulation results are shown for different fractional orders in the first stage. Finally, a number of graphical results of fractal-fractional MPX transmission models are presented showing the combined effect of fractal and fractional orders on model dynamics. The resulting simulations conclude that the new fractal-fractional operator added more biological insight into the dynamics of illness.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/mbe.2023287","type":"journal-article","created":{"date-parts":[[2023,2,4]],"date-time":"2023-02-04T11:18:28Z","timestamp":1675509508000},"page":"6666-6690","source":"Crossref","is-referenced-by-count":48,"title":["Analysis of Monkeypox viral infection with human to animal transmission via a fractional and Fractal-fractional operators with power law kernel"],"prefix":"10.3934","volume":"20","author":[{"given":"Alia M.","family":"Alzubaidi","sequence":"first","affiliation":[{"name":"Department of Mathematics, AL-Qunfudhah University college, Umm Al-Qura University, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hakeem A.","family":"Othman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, AL-Qunfudhah University college, Umm Al-Qura University, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Saif","family":"Ullah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nisar","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Institute of Numerical Sciences Kohat University of Science and Technology (KUST) Kohat, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohammad Mahtab","family":"Alam","sequence":"additional","affiliation":[{"name":"Department of Basic Medical Sciences, College of Applied Medical Science, King Khalid University, Abha 61421, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2321","reference":[{"key":"key-10.3934\/mbe.2023287-1","unstructured":"<i>World Health Organization<\/i>, Monkeypox, 2022. 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