A fragment is a group of words similar to a sentence in the sense that it starts with a capital letter and ends with an end mark but that in reality, it is not a sentence as it does not convey a complete idea. In this sense, a fragment is more like a phrase or a dependent clause, but standing alone.
<em>Hoping to beat his time from last year. </em>is a fragment because it does not express a complete thought. In order to correct it, we must add an independent or main clause that contains a subject, for example:
Hoping to beat his time from last year, <u>Theo</u> was determined to work even harder this time.
