Solvability of the infinite systems of nonlinear third-order differential equations in the weighted sequence space mω(∆ςv, ψ, q)

In this work, we first introduce the concept of weighted sequence space mω(∆ςv, ψ, q). Then, we construct a Hausdorff measure of noncompactness on this sequence space. Furthermore, by employing this measure of noncompactness we discuss the solvability of an infinite system of nonlinear third-order differential equations with initial conditions in the weighted sequence space mω(∆ςv, ψ, q). Eventually, we demonstrate an example to show the usefulness of the obtained result..