Fitting two different data sets with the same parameters

Hello Everyone,
I have a question about fitting two different datasets with the same fitting parameters.
I have a decay plot for two different peaks, individually if I fit them I get two different decay times from the fits, I want to fit both of them at once with the same parameters so that I can have only one decay time. Is there any way to solve this issue?
Below you can see the plot, each of them is individually fitted with different parameters.

Thank you for your time
Screenshot from 2021-03-08 14-13-05

There exist some “Fit Tutorials” in ${ROOTSYS}/tutorials/fit/ which demonstrate how to fit several histograms or graphs simultaneously, e.g.:


Thank you very much.