Common fixed points of a pair of \((\psi ,\phi )\)-weakly contractive maps via ceiling distance with applications

In this paper, we discuss a critical analysis of a paper by Kumar (J Comput Appl Math 404:1–16 2022), found some corrections through the use of examples, demonstrating inaccuracies in the established results, hereafter we introduce the concept of w-generalized \((\psi ,\phi )\) $(\psi ,\varphi )$ -weakly contractive maps and formulate some common fixed point theorems that incorporate weak altering distance and ceiling distance functions. Furthermore, to demonstrate the applicability of obtained results, some examples and applications involving systems of nonlinear fractional differential equations, Fredholm integral equations, and boundary value problems are provided.