Analytical solution of Atangana-Baleanu fractional viscoelastic relaxation model – Laplacian approach

Abstract

In this contribution, a new novel approach based on the Atangana-Baleanu fractional in conjunction with the Laplacian approach is utilized to obtain an analytical solution of a fractional time relaxation viscoelastic model. The fractional time relaxation model is based on the upper convected Maxwell constitutive relaxation equation. Results for the existence and uniqueness of the solution are presented. Analytical expressions of the solutions are obtained for the underlying physical time relaxation viscoelastic model. Two test model problems with prescribed initial conditions are used to investigate the intricate behaviour of the viscoelastic two-dimensional fluid. The influence of key parameters such as relaxation time, Reynolds number and the order of the fractional derivative on fluid flow characteristics is analyzed and discussed.