Baleanu, D.Alzaidy, J. F.Hashemizadeh, E.Zaky, M. A.02.02. Matematik02. Fen-Edebiyat Fakültesi01. Çankaya Üniversitesi2019-12-232025-09-182019-12-232025-09-182018Zaky, M. A...et al. (2018). "Operational matrix approach for solving the variable-order nonlinear Galilei invariant advection-diffusion equation", Advances in Difference Equations.1687-1847https://doi.org/10.1186/s13662-018-1561-7https://hdl.handle.net/20.500.12416/13423Zaky, Mahmoud/0000-0002-3376-7238In 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/s13662-018-1561-72-s2.0-85044267938