<p>In recent years, fractional-order models have attracted considerable interest due to their enhanced capability to describe complex dynamical behaviors more accurately than classical integer-order formulations. Motivated by this, the present work studies quadratic and cubic logistic growth models governed by fractional derivatives with singular kernels. This study relies on a recently developed framework of fractional derivatives, where the derivative operator is defined as an appropriate inverse of a convolution-type integral operator associated with a Prabhakar kernel. Within this context, we investigate the existence and uniqueness of solutions for the formulated models and construct a numerical scheme to approximate their solutions. We conduct a detailed analysis of the stability and convergence of the proposed scheme. Furthermore, we present numerical simulations for various fractional extensions of logistic models, emphasizing numerical approximation comparisons between the solutions obtained using the newly introduced singular kernel derivative and those based on the classical Caputo derivative.</p>