In the current article we obtain the extension of Darbo’s fixed point theorem (DFPT), and apply this theorem to prove the existence of solution of an infinite system of implicit fractional integral equations. We, besides that, justify the results with the help of an example. The advantage of the proposed fixed point theory is that the requirement of the compactness of the domain is relaxed which is essential in some fixed point theorems. Also, we have applied it to integral equation involving fractional integral by another function which is a generalization of many fixed point theorems as well as fractional integral equations. © 2021, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.