<p>This paper proposes a novel piecewise hybrid Caputo fractional–stochastic framework for the analysis of a Cauchy problem arising in complex biological systems. The hybrid framework couples a deterministic Caputo fractional derivative over an initial interval with a fractional stochastic differential operator over a subsequent interval. This allows the system to exhibit transitions between memory-dominated and noise-dominated regimes that are not captured by classical or uniformly fractional models. A well-defined solution operator is introduced for the hybrid system, thereby ensuring the mathematical well-posedness of the associated Cauchy problem. Using fixed-point theorem , the existence, uniqueness, and continuous dependence of mean-square solutions are rigorously proved. In addition, an appropriate numerical method is developed to enable the solution of such problems. Furthermore, the Ulam–Hyers stability of the proposed hybrid system is also established, ensuring the robustness of solutions under small perturbations. The key contribution of this work lies in the development of a piecewise Caputo fractional–stochastic framework that rigorously integrates deterministic memory effects with stochastic perturbations within a single Cauchy problem. The practical relevance of the proposed approach is further highlighted through the case study of the dynamics of Tomato Yellow Leaf Curl disease.</p>