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Using a combined state and parameter estimation approach, we develop an algorithm serving to estimate simultaneously, the system parameters, the system orders, and the system states. By minimizing the defining criterion, which is non-convex and nonlinear in the parameters, the model parameters are estimated using the recursive least squares and the Levenberg\u2013Marquardt algorithms. Next, the system states are estimated using the Luenberger observer. Then, the convergence analysis of the proposed algorithm is proved. Finally, the Monte Carlo simulation analysis and an application to Ultracapacitor system are used to demonstrate the effectiveness of the suggested method.<\/jats:p>","DOI":"10.1177\/09596518231171226","type":"journal-article","created":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T07:31:32Z","timestamp":1683876692000},"page":"1853-1866","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":11,"title":["On the combined estimation of the parameters and the states of fractional-order systems"],"prefix":"10.1177","volume":"237","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6003-2376","authenticated-orcid":false,"given":"Soumaya","family":"Marzougui","sequence":"first","affiliation":[{"name":"Research Laboratory of Numerical Control of Industrial Processes, National Engineering School of Gabes, University of Gabes, Gabes, 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