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Mathematical model of the\nsystem is a second\u2010order differential equation with a nonlinearity of polynomial type, whose terms are of integer and\/or noninteger order. For the\ncase when only one nonlinear term exists, the exact analytical solution of\nthe differential equation is determined as a cosine\u2010Ateb function. Based on this solution, the asymptotic averaging procedure for solving the perturbed strong non\u2010linear differential equation is developed. The method does not require the existence of the small parameter in the system. Special attention is given to the case when the dominant term is a linear one and to the case when it is of any non\u2010linear order. Exact solutions of\nthe averaged differential equations of motion are obtained. The obtained results\nare compared with \u201cexact\u201d numerical solutions and previously obtained\nanalytical approximate ones. Advantages and disadvantages of the suggested\nprocedure are discussed.<\/jats:p>","DOI":"10.1155\/2012\/649050","type":"journal-article","created":{"date-parts":[[2012,2,22]],"date-time":"2012-02-22T21:03:37Z","timestamp":1329944617000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":49,"title":["Oscillator with a Sum of Noninteger\u2010Order Nonlinearities"],"prefix":"10.1155","volume":"2012","author":[{"given":"L.","family":"Cveticanin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T.","family":"Pog\u00e1ny","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2012,2,22]]},"reference":[{"key":"e_1_2_7_1_2","first-page":"718","article-title":"The asymptotic method and periodic\nAteb functions in the investigation of some nonlinear wave equations","volume":"18","author":"Sokil B. 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