Caputo q-Fractional Initial Value Problems and a q-Analogue   Mittag-Leffler Function
  Caputo q-fractional derivatives are introduced and studied. A Caputo -type q-fractional initial value problem is solved and its solution is expressed by means of a new introduced q-Mittag-Leffler function. Some open problems about q-fractional integrals are proposed as well. 
Thabet Abdeljawad, Dumitru Baleanu
math.DS