In the present work, parameters for adapting the behavior of the uniaxial three-element viscoelastic constitutive model with integer and fractional index derivatives to the mechanical evolution of an epoxy-composite material reinforced with long random henequen fibers, were determined. Cyclic loading–unloading with (Formula presented.), (Formula presented.), (Formula presented.), …, (Formula presented.) controlled strain and staggered fluency experiments at 5 MPa, 10 MPa, and 15 MPa constant tension were performed in stages, and the obtained data were used to determine and validate the model’s parameter values. The Inverse Method of Identification was used to calculate the parameters, and the Particle Swarm Optimization (PSO) method was employed to achieve minimization of the error function. A comparison between the simulated uniaxial results and the experimental data is demonstrated graphically. There exists a strong dependence between properties of the composite and the fiber content (0 wt%, 9 wt%, 14 wt%, 22 wt%, and 28 wt% weight percentage fiber/matrix), and therefore also of the model parameter values. Both uniaxial models follow the viscoelastic behavior of the material and the fractional index version presents the best accuracy. The latter method was noted to be adequate for determination of the aforementioned constants using non-large experimental data and procedures that are easy to implement.