{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T22:38:53Z","timestamp":1784673533993,"version":"3.55.0"},"reference-count":69,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,10,22]],"date-time":"2020-10-22T00:00:00Z","timestamp":1603324800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100009509","name":"Kementerian Riset Teknologi Dan Pendidikan Tinggi Republik Indonesia","doi-asserted-by":"publisher","award":["037\/ SP2H\/LT\/ DRPM\/ 2020"],"award-info":[{"award-number":["037\/ SP2H\/LT\/ DRPM\/ 2020"]}],"id":[{"id":"10.13039\/501100009509","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The harvesting management is developed to protect the biological resources from over-exploitation such as harvesting and trapping. In this article, we consider a predator\u2013prey interaction that follows the fractional-order Rosenzweig\u2013MacArthur model where the predator is harvested obeying a threshold harvesting policy (THP). The THP is applied to maintain the existence of the population in the prey\u2013predator mechanism. We first consider the Rosenzweig\u2013MacArthur model using the Caputo fractional-order derivative (that is, the operator with the power-law kernel) and perform some dynamical analysis such as the existence and uniqueness, non-negativity, boundedness, local stability, global stability, and the existence of Hopf bifurcation. We then reconsider the same model involving the Atangana\u2013Baleanu fractional derivative with the Mittag\u2013Leffler kernel in the Caputo sense (ABC). The existence and uniqueness of the solution of the model with ABC operator are established. We also explore the dynamics of the model with both fractional derivative operators numerically and confirm the theoretical findings. In particular, it is shown that models with both Caputo operator and ABC operator undergo a Hopf bifurcation that can be controlled by the conversion rate of consumed prey into the predator birth rate or by the order of fractional derivative. However, the bifurcation point of the model with the Caputo operator is different from that of the model with the ABC operator.<\/jats:p>","DOI":"10.3390\/axioms9040122","type":"journal-article","created":{"date-parts":[[2020,10,22]],"date-time":"2020-10-22T10:27:58Z","timestamp":1603362478000},"page":"122","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["A Rosenzweig\u2013MacArthur Model with Continuous Threshold Harvesting in Predator Involving Fractional Derivatives with Power Law and Mittag\u2013Leffler Kernel"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0118-2745","authenticated-orcid":false,"given":"Hasan S.","family":"Panigoro","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang 65145, Indonesia"},{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, State University of Gorontalo, Bone Bolango 96119, Indonesia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1335-5631","authenticated-orcid":false,"given":"Agus","family":"Suryanto","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang 65145, Indonesia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7307-1537","authenticated-orcid":false,"given":"Wuryansari Muharini","family":"Kusumawinahyu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang 65145, Indonesia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4163-8030","authenticated-orcid":false,"given":"Isnani","family":"Darti","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang 65145, Indonesia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1086\/282272","article-title":"Graphical representation and stability conditions of predator-prey interactions","volume":"97","author":"Rosenzweig","year":"1963","journal-title":"Am. 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