MONOTONE ITERATIVE TECHNIQUE FOR FRACTIONAL MEASURE DIFFERENTIAL EQUATIONS IN ORDERED BANACH SPACE

This article is based on the monotonic iterative method in the presence of upper and lower solutions, and investigates the existence of Sasymptotic u- periodic mild solutions for a class of fractional measure differential equations with nonlo cal conditions in an ordered Banach spaces. Firstly, in the case of upper and lower solutions, a monotonic iterative method is constructed to obtain the maximal and minimal Sasymptotically u- periodic mild solution to our concern problem. Secondly, we establish an existence result of Sasymptotically u- periodic mild solutions for the mentioned without assuming the existence of upper and lower Sasymptotically u- periodic mild solutions under generalized monotonic conditions and non compactness measure conditions of nonlinear terms. Finally, as an application of abstract results, an example is provided to illustrate our main findings.