Can I ask the author of the research paper to use his program in my research?
I am a researcher in the computer science field, and I'd say it's not unusual to ask authors of published papers for their code/applications. Sometimes, however, people might be reluctant to give you the software, because research code is often unstable and badly documented, and they might be ashamed (or worried that you will find bugs that could invalidate their previous publications!).

You should surely contact the authors, explain the situation, and stress that you are (of course) going to cite their paper. There's no harm in asking. In my experience, the worst-case scenarios are:
a) they will not reply;
b) they will reply, and ask you to be included among the authors of your future paper, in exchange for the software.

You could try to prepare for these two outcomes, while hoping for a positive answer :-)