On some properties of Riemann-Liouville fractional operator in Orlicz spaces and applications to quadratic integral equations

Abstract

This article demonstrates some properties of the Riemann-Liouville (R-L) fractional integral operator like acting, continuity, and boundedness in Orlicz spaces L?. We apply these results to examine the solvability of the quadratic integral equation of fractional order in L?. 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 ??, ?2, or ?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.