Nonlinear implicit fractional differential equation involving -Caputo fractional derivative

In this paper, we consider a nonlinear implicit fractional di erential equation with nonlocal condition and involving the Caputo fractional derivative with respect to another function. We investigate the existence, uniqueness of solution on subinterval of the original interval. Hence we give an estimation for this solution. Further, we discuss the continuous dependence of solution involved in the problem. The results obtained by means of a variety of tools fractional calculus including Banach contraction mapping principle. Illustrative examples are also given.