Zaky, M. A.Baleanu, DumitruAlzaidy, J. F.Hashemizadeh, E.2019-12-232019-12-232018Zaky, M. A...et al. (2018). "Operational matrix approach for solving the variable-order nonlinear Galilei invariant advection-diffusion equation", Advances in Difference Equations.1687-1847http://hdl.handle.net/20.500.12416/2242In this paper, we investigate numerical solution of the variable-order fractional Galilei advection-diffusion equation with a nonlinear source term. The suggested method is based on the shifted Legendre collocation procedure and a matrix form representation of variable-order Caputo fractional derivative. The main advantage of the proposed method is investigating a global approximation for the spatial and temporal discretizations. This method reduces the problem to a system of algebraic equations, which is easier to solve. The validity and effectiveness of the method are illustrated by an easy-to-follow example.eninfo:eu-repo/semantics/openAccessVariable-Order DerivativeNonlinear Galilei Invariant Advection-Diffusion EquationCollocation MethodLegendre PolynomialsArticle10.1186/s13662-018-1561-7