An existence result for an infinite system of implicit fractional integral equations via generalized Darbo's fixed point theorem

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.

Automated summary

In this article, we extend Darbo's fixed point theorem and use it to prove the existence of solutions for an infinite system of implicit fractional integral equations. The proposed fixed point theory relaxes the requirement of compactness of the domain, which is essential in some fixed point theorems. Additionally, we apply it to integral equations involving fractional integrals, which generalizes many fixed point theorems and fractional integral equations.