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In this respect, all possible equilibria and their existence conditions are determined and their stability properties are established. We also construct nonstandard numerical schemes based on Gr\u00fcnwald-Letnikov approximation. The constructed scheme is explicit and maintains the positivity of solutions. Using this scheme, we perform some numerical simulations to illustrate the dynamical behavior of the model. It is noticed that the nonstandard Gr\u00fcnwald-Letnikov scheme preserves the dynamical properties of the continuous model, while the classical scheme may fail to maintain those dynamical properties.<\/jats:p>","DOI":"10.1155\/2017\/8273430","type":"journal-article","created":{"date-parts":[[2017,5,28]],"date-time":"2017-05-28T21:01:13Z","timestamp":1496005273000},"page":"1-9","source":"Crossref","is-referenced-by-count":18,"title":["Stability Analysis of a Fractional Order Modified Leslie-Gower Model with Additive Allee Effect"],"prefix":"10.1155","volume":"2017","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1335-5631","authenticated-orcid":true,"given":"Agus","family":"Suryanto","sequence":"first","affiliation":[{"name":"Department of Mathematics, Brawijaya University, Jl. 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