Abstract
As it is not always true that the distance between the points in fuzzy rectangular metric spaces is one, so we introduce the notions of rectangular and b-rectangular metric-like spaces in fuzzy set theory that generalize many existing results, which can be regarded as the main advantage of this paper. In these spaces, the symmetry property is preserved, but the self distance may not be equal to one. We discuss topological properties and demonstrate that neither of these spaces is Hausdorff. Using alpha-psi-contraction and Geraghty contractions, respectively, in our main results, we establish fixed point results in these spaces. We present examples that justify our definitions and results. We use our main results to demonstrate that the solution of a nonlinear fractional differential equation for HIV is unique.