Abstract
In this paper, we consider a coupled system of sequential fractional differential equations associated with initial conditions. The main theorems provide new existence and uniqueness conditions for solutions of the proposed coupled system. We conclude an immediate consequence that establishes weaker conditions to ensure the existence and uniqueness of solutions for the corresponding sequential fractional differential equation. Meanwhile, an iterative sequence is constructed in terms of solution operator that converges to the unique fixed point which corresponds to the unique solution. The consistency of the main results is verified by presenting two numerical examples. For the sake of completeness, we end the paper with a concluding remark.