Solvability of an infinite system of $ n $-th order differential equations in a paranormed sequence space and its numerical solution

In this paper, we introduce a ball measure of noncompactness in the Banach sequence space $ bv_q $ $ (1\leq q < \infty) $ containing the space $ l_q $. By applying the technique of measures of noncompactness and Meir–Keeler condensing mappings, we investigate the existence of solutions of an infinite system of differential equations of order $ n $ with boundary conditions. Some examples are provided to support our main results. A numerical spectral method based on Bernoulli polynomials is applied to find the approximate solution of an example.