Oscillation criteria for generalized Emden-Fowler equations via local generalized derivatives and Mittag-Leffler kernels

Abstract

This paper investigates the oscillatory behavior of a generalized
version of the Emden-Fowler equation using the Local Generalized Derivative (LGD). We establish a new generalized Riccati identity and use the Divergence Theorem to derive an energy inequality for non-oscillatory solutions. By introducing a radial scaling function and a generalized Hartman-Wintner criterion, we demonstrate how the choice of the kernel function, specifically the Mittag-Leffer kernel, drastically alters the stability of the system, compared to classical conformable models. Our results show that exponential kernels can induce ``ultra-sensitive" oscillations even when the potential function decays, providing a more flexible framework for modeling complex physical media.