On Some Properties of Riemann-Liouville Fractional Operator in Orlicz Spaces and Applications to Quadratic Integral Equations

This article demonstrates some properties of the Riemann-Liouville (R-L) fractional integral operator like acting, continuity, and boundedness in Orlicz spaces L phi. We apply these results to examine the solvability of the quadratic integral equation of fractional order in L phi. Because of the distinctive continuity and boundedness conditions of the operators in Orlicz spaces, we look for our concern in three situations when the generating N-functions fulfill increment ', increment 2, or increment 3-conditions. We utilize the analysis of the measure of noncompactness with the fixed point hypothesis. Our hypothesis can be effectively applied to various fractional problems.