Applications of a new measure of noncompactness to the solvability of systems of nonlinear and fractional integral equations in the generalized Morrey spaces

This article introduces a measure of noncompactness in the generalized Morrey space. We study the applications of our new definition in investigating the conditions for the existence of solutions for systems of nonlinear integral equations. We can extend many useful theorems in \(L^{p}(\mathbb {R}^{N})\) $L^p({\mathbb{R}}^N)$ for functions belonging to the generalized Morrey spaces. Compared to the \(L^{p}(\mathbb {R}^{N})\) $L^p({\mathbb{R}}^N)$ spaces, the advantage of studying in the Morrey spaces is that we can research no compact support functions in our problems. Finally, significant examples are presented to show the efficiency of the main results.