Stability Analysis of Fractional-Order Stochastic Differential Equations with Levy ´ Noise

Abstract

In this paper, we investigate the generalized Mittag-Leffler-Hyers-Ulamstability of fractional-order stochastic differential equations with finite de-lays, incorporating Levy noise and employing the Caputo derivative for ´1 < ℘ < 2. By applying fractional calculus and Gronwall-type inequalities,we establish stability results in the senses of Hyers–Ulam, Rassias, and theirgeneralized forms. To validate the results, numerical methods are employed,specifically the Euler–Maruyama scheme for the stochastic components anda heuristic Euler-type approach scaled by dt℘ to approximate the fractionalderivative. The MATLAB-generated graphs illustrate the solution behav-ior under different stochastic influences, highlighting the practical relevanceand effectiveness of the findings.