University of TabrizComputational Methods for Differential Equations2345-398212120241101A one-step algorithm for strongly non-linear full fractional duffing equations1171351631710.22034/cmde.2023.53596.2256ENJafarBiazarDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 41335-1914, P.C.4193822697, Rasht, Iran.0000-0001-8026-2999HamedEbrahimiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box
41335-1914, P.C.4193822697, Rasht, Iran.0000-0003-0462-4729Journal Article20220927In 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