Dear Dr Erman,

Thank you for your response. However, that was not exactly the method I was looking for. I already solved my FDE analytically. Now, I intend to estimate the main parameters of the model (for example by using nonlinear regression) and validate the model with diffusion experimental data. The fractional order of my FDE is being considered one of the parameters. I'm facing some problems in doing that. That's why I posted a question here. I would like to know if there's a proper estimation method to treat problems based on FDE. 

Thank you again for your response.

Sincerely,

Douglas J. Nicolin

Dear Douglas J. Nicolin

I think you took the fractional order parameter  between [0,1], and you found that the experimental data tend to fit with the curve when the parameter=1, so to get the optimal value of this parameter, try to change the parameter interval  to become [1,2] and solve the FDE again. If you get the same result then, the optimal value of the parameter=1