In Arabic and Islamic studies I would strongly recommend including both the Hijrī and Gregorian years, especially when dealing with mediaeval and classical periods. It is important to adhere to a standard dating format.
I strongly recommend including dates of death for all significant personalities and authors referred to. Firstly, for the obvious reason that your reader knows which time period is being discussed and secondly to avoid confusion as there are numerous authors from different periods with the same name (Ibn al-Athīr for example).
If you do not know both dates you can use websites which allow you to convert Hijri to Gregorian and vice versa. While a margin of error remains if you do not know the exact date, the most you can be off by is a few months. You can use either http://www.islamweb.net/ver2/engblue/date_converter.php or http://www.rabiah.com/convert/ or any one of the other sites out there
- It is crucial that you disambiguate your dating format in a note after the acknowledgments page. This is how my note on dating read: ‘Dates are given in the format (xxxx/yyyy), where xxxx is the Hijrī year and yyyy is the Gregorian year.’
- The date format I used in my dissertation was Xth/Yth century-where X is the century according to the Hijrī calendar and Y is the century according to the Gregorian calendar, for example: ‘the Fatimid phase (4th–6th/10th-12th century)’.
- For more specific dates such as year of authorship, birth, war or death etc. I used the format (XXXX/YYYY), where XXXX is the year according to the Hijrī calendar and YYYY is the year according to the Gregorian calendar. So in the case of an author’s date of death: “Barā ͨat al-istihlāl is defined by al-Suyūṭī (d. 911/1505) as an opening that ‘befits the state of the speaker and alludes to the reason for the speech’.”
- I (eventually came to) use this system because writing AH after each Hijrī date and AD or CE after each Gregorian date is not only cumbersome, breaking the flow of the sentence, but it also consumes precious ‘words’. In the format (911 AH/1505 AD) you consume four words from your word-limit while the (d. 911/1505) you consume only two. If you write 1st century AH/ 7th century AD you consume six words while if you write 1st/7th century you consume only two.
As always, whichever system you use, be consistent!