University of Guilan Journal of Mathematical Modeling 2345-394X 9 1 2021 01 01 Solving the Basset equation via Chebyshev collocation and LDG methods 61 79 4231 10.22124/jmm.2020.17135.1489 EN Mohammad Izadi Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran Mehdi Afshar Department of Mathematics and Statistics, Zanjan Branch , Islamic Azad University, Zanjan, Iran. Journal Article 2020 07 18 Two different numerical methods are developed to find  approximate solutions of a class of linear fractional differential equations (LFDEs) appearing in the study of the generalized Basset force, when a sphere sinks in a viscous fluid. In the first one, using the Chebyshev bases, the collocation points, and the matrix operations, the given LFDE reduces to a matrix equation while in the second one, we employ the local discontinuous Galerkin (LDG) method, which uses the natural upwind flux yielding a stable discretization. Unlike the first method, in the latter method we are able to solve the problem element by element locally and there is no need to solve a full global matrix. The efficiency of the proposed algorithms are shown via some numerical examples. https://jmm.guilan.ac.ir/article_4231_c43909580b688d457545bf3290f7da3e.pdf