Construction of a measure of noncompactness in Sobolev spaces with an application to functional integral-differential equations

In this paper, first we introduce a measure of noncompactness in the Sobolev space W k , 1 ( Ω ) and then, as an application, we study the existence of solutions for a class of the functional integral-differential equations using Darbo’s fixed point theorem associated with this new measure of noncompactness. Further, two examples are presented to verify the effectiveness and applicability of our main results.