University of Tabriz Computational Methods for Differential Equations 2345-3982 10 4 2022 10 01 Asymptotic method for solution of oscillatory fractional derivative 1123 1130 13860 10.22034/cmde.2021.46895.1973 EN Fikret Ahmadali Aliev Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan. Institute of Information Technologies of the National Academy of Sciences of Azerbaijan. Nihan Aliev Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan. Nazile Hajiyeva Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan. Nargiz Safarova Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan. Rufana Aliyeva Nakhchivan State University, Nakhchivan, Azerbaijan. Journal Article 2021 07 17 In the paper, an oscillatory system with liquid dampers is considered, when the mass of the head is large enough. By means of expedient transformations, the equation of motion with fractional derivatives is reduced to an equation of fractional order containing a small parameter. The corresponding nonlocal boundary value problem is solved and the zero and first approximations of solutions of the relative small parameter are constructed. The results are illustrated on the concrete example, where the solution differs from the analytical solution by 10−2 order.  https://cmde.tabrizu.ac.ir/article_13860_aa1be6fdc00c4f017daae4119a671464.pdf