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

Journal of inequalities and applications

Hemant Kumar Nashine¹ 

关键词: measures of noncompactness;    Darbo’s fixed point theorem;    coupled fixed point;    integral equations;    47H10;    54H25;   

DOI  :  10.1186/s13660-017-1497-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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 et al. (J. Comput. Appl. Math. 260:67-77, 2014)), (Aghajani et al. (Bull. Belg. Math. Soc. Simon Stevin 20(2):345-358, 2013)), (Arab (Mediterr. J. Math. 13(2):759-773, 2016)), (Banaś et al. (Dyn. Syst. Appl. 18:251-264, 2009)), and (Samadi et al. (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.

【 授权许可】

CC BY