Laplace inverse and MR approach to existence of a unique solution and the Hyers–Ulam–Wright stability analysis of the nonhomogeneous fractional delay oscillation equation by matrix-valued fuzzy controllers

In this paper, we consider the nonhomogeneous fractional delay oscillation equation with order κ and investigate the existence of a unique solution in matrix-valued fuzzy Banach spaces for this equation using the alternative fixed point theorem. In a fuzzy environment, we introduce a class of the matrix-valued fuzzy Wright controller to investigate the Hyers–Ulam–Wright stability for the NH-FD-O equation with order κ . Finally, an illustrative example to demonstrate the application of the main theorem is also considered.