Successive approximation method for Caputo q-fractional IVPs

• This paper studies the convergence of the Caputo q-fractional initial value problem.
• It is studied under the q-Krasnoselskii–Krein type condition for the first time.
• The aim is to handle the missing convergence investigation in ref [1].

Recently, Abdeljawad and Baleanu (2011) introduced Caputo q-fractional derivatives and used it to solve Caputo q-fractional initial value problem. For this purpose, they applied successive approximation method to obtain an explicit solution; but did not clarify under which conditions that this method will be convergence. In this paper, we propose q-Krasnoselskii–Krein type condition to investigate the convergence of the method.