In this manuscript, the measure of noncompactness, the fixed-point theorem, as well as fractional calculus, are used to carry out the analysis of the solvability of a product of $n$-quadratic Erdélyi-Kober ( $\mathcal{E}\mathcal{K}$) fractional-type integral equations in Orlicz spaces $L_{\phi }$. Several qualitative properties of the solution for the studied problem are established, such as the existence, monotonicity, uniqueness, and continuous dependence on the data. We conclude with some examples that illustrate our hypothesis.