The field fractional partial differential equations has been greatly expanding with in the last 20 years as evidenced by the growing body of literature. The work has primarily been theoretical in nature as there has been limited availability of experimental data. This work demonstrates using simulated data, how one can utilize these models and apply them to real world data to make inferences about the parameter values, predictions at future values and even what forcing mechanism was used to generate the data. This is done using a Bayesian approach that employs Markov chain Monte Carlo techniques. The proposed approach is evaluated using simulation studies concerning credible interval coverage probabilities and highest posterior model probabilities. The simulation study shows that the proposed method is effective for many parameters and that more work is needed to better estimate some physical coefficients.