Local attractivity and stability analysis of a nonlinear quadratic fractional integral equation

Abstract

The authors prove two local attractivity and asymptotic stability results for a hybrid functional nonlinear fractional integral equation under weak Lipschitz and compactness type conditions. It is shown that comparable solutions of the equation are uniformly locally ultimately attractive and asymptotically stable on unbounded intervals of the real line. Their proofs rely on a recent measure theoretic fixed point theorem of Dhage.