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 $L_\varphi$. We apply these results to examine the solvability of the quadratic integral equation of fractional order in $L_\varphi$.
Because of the distinctive continuity and boundedness conditions of the operators in Orlicz spaces, we look at our concern in three situations when the generating $N$-functions fulfilling $\Delta',~\Delta_2$, or $\Delta_3$-conditions. We utilize the analysis of the measure of noncompactness with the fixed point hypothesis. Our hypothesis can be effectively applying to various fractional problems.