How I can create a conceptual framework of banking regulation, financial stability and technical efficiency to compare Islamic banks and traditional banks in Mauritania ?
I think that you need to decide your approach as to whether regulation enhances financial stability or does not and take a similar view on the interaction between regulation and efficiency. One approach would be to have a hypothesis that that regulation enhances stability but that this may be at the expense of efficiency. In any case you have all three as variables in a potential analysis.
What I did to look at longitudinal changes was to do a series of data envelopment analysis studies and then use the Malmquist index. I could then track technical efficiency over time.
The early work is in this doument: https://www.clmr.unsw.edu.au/sites/default/files/content_files/cifr_report_aug_2015.pdf
I have refined it for peer review publication with my colleague Professor Deborah Healey and can send those papers, if that would be useful.
you can test the effect of the banking regulation (deregulation) on banks' efficiency by investigating the efficiency before and after the period of regulation (deregulation), and make the comparison.
This article may be useful for your project. it investigates the efficiency of Algerian banks in the post-liberalization period. https://www.researchgate.net/publication/313853969_EFFICIENCY_OF_THE_ALGERIAN_BANKS_IN_THE_POST_LIBERALIZATION_PERIOD
Article EFFICIENCY OF THE ALGERIAN BANKS IN THE POST LIBERALIZATION PERIOD