On Erdlyi-Kober Fractional Operator and Quadratic Integral Equations in Orlicz Spaces

We provide and prove some new fundamental properties of the Erdelyi-Kober (EK) fractional operator, including monotonicity, boundedness, acting, and continuity in both Lebesgue spaces (L-p) and Orlicz spaces (L-phi). We employ these properties with the concept of the measure of noncompactness (MNC) associated with the fixed-point hypothesis (FPT) in solving a quadratic integral equation of fractional order in L-p, p >= 1 and L-phi. Finally, we provide a few examples to support our findings. Our suppositions can be successfully applied to various fractional problems.