In this paper, we have introduced a Generalized Biparametric Family of Conformable Vectorial Advanced Method (GBCOVAM) using the conformable derivative to find simple roots of a system of nonlinear equations, allowing the conformable derivative \(\mathbb {T}_p^\theta \phi (s)\) equal zero in the neighborhood of desired roots. Iterative methods using conformable derivatives minimize the number of iteration steps and increase stability as compared to existing methods. To verify the theoretical results, we consider problems arising from chemical engineering applications, other applied models, and standard academic test problems. The convergence analysis of GBCOVAM needs conformable Fréchet derivatives; thus, we have newly developed conformable order Fréchet derivatives to study broadly the proposed methods. Also, the notion of Approximated computational Order of Convergence (ACOC) is used to verify the theoretical convergence. Moreover, for better understanding, the convergence and dynamical planes are visualized on a three-dimensional Riemann sphere.
