A numerical method for the transient couette flow of a distributed-order viscoelastic fluid

This work presents a numerical method for the solution of two coupled distributed-order fractional differential equations, that appear in the pure tangential flow of fluids modelled by the Distributed-Order Viscoelastic Model. We prove the solvability of the method, and, perform numerical simulations of relaxation tests.Supported by FCT - Fundacao para a Ciencia e a Tecnologia, through projects: UIDB/00013/2020 and UIDP/00013/2020 (CMAT - Centre of Mathematics - University of Minho); UIDB/04621/2020 and UIDP/04621/2020 (CEMAT/IST-ID, Center for Computational and Stochastic Mathematics, Instituto Superior Tecnico, University of Lisbon). This work was also partially supported by FCT through the project UIDB/00297/2020 (Centro de Matem ' atica e Aplicacoes)