On \(L_\phi \) -Solutions for n-Product of Fractional Integral Operators

The presented article studies the existence results for the n-product of fractional nonlinear equations in Orlicz spaces \(L_\varphi \) . As a result of employing various types of growth conditions, we can consider a wide variety of boundedness and continuity assumptions of the studied operators in \(L_\varphi \) (they do not need to be Banach algebras). We analyze three different existence theorems related to the generating N-functions realize \(\Delta ',~\Delta _3\) , or \(\Delta _2\) -conditions on the product of different n-Orlicz spaces. An adequate measure of noncompactness (MNC) and fixed point hypothesis (FPT) are our main tools to attain the outcomes.