In this article, some new generalizations of Darbo’s fixed-point theorem are given and the solvability of an infinite system of weighted fractional integral equations of a function with respect to another function is studied. Also, with the help of a proper example, we illustrate our findings.

In 2014, Zead Mustafa introduced b(2)-metric spaces, as a generalization of both 2-metric and b-metric spaces. Then new fixed point results for the classes of rational Geraghty contractive mappings of type I, II and III in the setup of b(2)-metric spaces are investigated. Then, we prove some fixed point theorems under various contractive conditions in partially ordered b(2)-metric spaces. These include Geraghty-type conditions, conditions that use comparison functions and almost generalized weakly contractive conditions. Berinde in [17-20] initiated the concept of almost contractions and obtained many interesting fixed point theorems. Results with similar conditions were obtained, e.g., in [21] and [22]. In the last section of the paper, we define the notion of almost generalized (psi, phi)(s,a)-contractive mappings and prove some new results. In particular, we extend Theorems 2.1, 2.2 and 2.3 of Ciric et.al. in [23] to the setting of b(2)-metric spaces. Also, some examples are provided to illustrate the results presented herein and several interesting consequences of our theorems are also provided. The findings of the paper are based on generalization and modification of some recently reported theorems in the literature.