Abstract
The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. For the first time, unsteady fractional Phan Thien Tanner fluid is modeled, which results in different space-time nonlinear fractional partial differential equations. All obtained fractional differential equations models have never been reported before in the literature. These mathematical models have been modeled by using the Mittag Leffler function, which helps to deduce some individual cases. Readers can use any analytical or numerical method to solve the modeled fractional differential equations.