University of Tabriz Computational Methods for Differential Equations 2345-3982 12 1 2024 11 01 A one-step algorithm for strongly non-linear full fractional duffing equations 117 135 16317 10.22034/cmde.2023.53596.2256 EN Jafar Biazar Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 41335-1914, P.C.4193822697, Rasht, Iran. Hamed Ebrahimi Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 41335-1914, P.C.4193822697, Rasht, Iran. Journal Article 2022 09 27 In the current study, a one-step numerical algorithm is presented to solve strongly non-linear full fractional duffing equations. A new fractional-order operational matrix of integration via  quasi-hat functions (QHFs) is introduced. Utilizing the operational matrices of QHFs, the main problem will be transformed into  a number of univariate polynomial equations. Absolute errors of the results in approximations and convergence analysis are addressed. Ultimately, five examples are provided to illustrate the capabilities of this algorithm. The numerical results are illustrated in some Tables and Figures, for different values of the parameters $\alpha~ and~ \beta$. https://cmde.tabrizu.ac.ir/article_16317_6b1d2c3cf524ceb9b297eec09829c912.pdf