Can you clarify your question ? Almost every customer shopping service uses recommender systems. Trust could have a variety of meanings based on the context. E.g. Trust as a measure of integrity, timeliness, accuracy, performance etc. Your question in its current form is vague.

Trust based recommender system that using trust to enhance recommended results. 

you can see real world trust recommendation system in many online shopping websites. It includes rating of service, products etc.

Epinions is a very popular source of data for recommender systems. many research papers are based on epinions data set

Even though we don't know which implementation real world recommender systems follow we know that trust-based recommendations use information derived from social ties. Thus, you should search for systems that have social networks (symmetric/asymmetric). In the following paper you can find the analysis of the most popular recommender systems in LBSNs.

https://www.researchgate.net/publication/283474388_A_Graph-Based_Taxonomy_of_Recommendation_Algorithms_and_Systems_in_LBSNs

Article A Graph-Based Taxonomy of Recommendation Algorithms and Syst...

Hi.  Also there is quite a lot of research out there that suggests that white box recommender solutions (those that explain how they got to the recommendation) foster more user trust than those that simply provide the recommendation in isolation.  An obvious real world example of this technique is "we recommend x because you bought y".