"In particular" is seen as the opposite of "In general". This is usually synonymous to "especially".
For example means As an example of..., this is synonymous to "For instance", "e.g" and "Such as".
Though "In particular" and "For example" may be used in similar cases, note that they do not have the same meaning. They may in some cases mean the same thing, but not always.
Cases with Different Meaning
The chancellor talked about the curriculum, the core courses in particular.
The orchestra was outstanding, the strings in particular
Here "in particular" cannot be replaced with "for example".
I can play quite a few musical instruments, for example, the flute, the guitar, and the piano.
Using "In particular" over here may change the meaning of the phrase. Using "In particular" may imply that the person is especially good at playing the flute, the guitar and the piano. Which may not necessarily be the case.
Cases with Similar Meaning
The book has quite a few plot holes. For example, it's never explained why the main character came to town to begin with.
Here "For example" may safely be replaced by "In particular".