Mittag-Leffler-Ulam stabilities for variable fractional-order differential equations driven by Lévy noise

This paper is devoted to investigating the existence and uniqueness of solutions, as well as Mittag-Leffler-Ulam stabilities for nonlinear variable fractional-order differential equations driven by L & eacute;vy noise. By establishing a novel set of suitable assumptions with the help of Picard iterations, we demonstrate the existence of unique solutions. Then, we investigate the stability of the considered fractional equations by applying the generalized Gronwall inequality and the definition of several types of stabilities, including Mittag-Leffler-Ulam-Hyers and Mittag-Leffler-Ulam-Hyers-Rassias stabilities. As an application, we present three illustrative examples attached with some numerical results to support the existing results.