Positive solutions of fractional integral equations by the technique of measure of noncompactness.

In the present study, we work on the problem of the existence of positive solutions of fractional integral equations by means of measures of noncompactness in association with Darbo's fixed point theorem. To achieve the goal, we first establish new fixed point theorems using a new contractive condition of the measure of noncompactness in Banach spaces. By doing this we generalize Darbo's fixed point theorem along with some recent results of (Aghajani (J. Comput. Appl. Math. 260:67-77, 2014)), (Aghajani (Bull. Belg. Math. Soc. Simon Stevin 20(2):345-358, 2013)), (Arab (Mediterr. J. Math. 13(2):759-773, 2016)), (Banaś (Dyn. Syst. Appl. 18:251-264, 2009)), and (Samadi (Abstr. Appl. Anal. 2014:852324, 2014)). We also derive corresponding coupled fixed point results. Finally, we give an illustrative example to verify the effectiveness and applicability of our results.