Solvability of generalized fractional order integral equations via measures of noncompactness

Abstract

In this article, we work on the existence of solution of generalized fractional integral equations of two variables. To achieve our main objective, we establish a new fixed point theorem using measure of noncompactness and a new contraction operator which generalized the Darbo’s fixed point theorem (DFPT). Also we obtain the corresponding coupled fixed point theorem. Finally we apply this generalized DFPT on the generalized fractional integral equations of two variables and illustrate our findings with the help of an example.