The single and multi-dimensional fractional neutral functional differential equations were studied by Agarwal and Baleanu in 2010, 2014, respec- tively. In this paper, we discuss the class of fractional neutral functional q{differential equations under in nite delay. In fact, our results are different applications of their main result in a sense on time scale. The Krasnosel- skii's xed point theorem is applied to obtain the existence of solution of the given problems. At the end, the examples which they contain some tables, gures and related algorithms with numerical effect, are added to show applications of the our results.
