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The application of fractional derivatives through Riemannliouville approach to xanthan gum viscoelasticity

Fractional derivatives are derivative with non-integer order, one of which is used for mathematical modeling of viscoelasticity. In this research, the fractional derivative was used to obtain a mathematical model of viscoelasticity. The method used was a fractional derivative through the Riemann-Liouville approach. The mathematical model of viscoelasticity obtained was a complex modulus consisting of storage and loss modulus. This model was applied to xanthan gum concentrate solution 0.5%, 1.0%, 2.0%, 3.0%, and 4.0% with simplified model parameters. The results obtained that the storage and loss modulus increased with increasing concentration of the solution. In addition, the modulus storage was always greater than the modulus loss for all concentrations of the solution. This suggests that the elastic properties of the xanthan gum solution are more dominant than their viscosity properties for all concentrations. Therefore, the viscoelasticity model using Riemann-Liouville fractional derivatives has a good ability to investigate the viscoelasticity behavior of all xanthan gum concentrations.  