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No previous study has involved uncertain delay differential equations with jump. In this paper, we consider the uncertain delay differential equations with V-jump, which is driven by both an uncertain V-jump process and an uncertain canonical process. First of all, we give the equivalent integral equation. Next, we establish an existence and uniqueness theorem of solution to the differential equations we proposed in the finite domain and the infinite domain, respectively. Once more, the concept of stability for uncertain delay differential equations with V-jump is proposed. In addition, the sufficient condition for stability theorem is derived. To judge existence, uniqueness, and stability briefly, we provide some examples in the end.

Existence, uniqueness, and stability of uncertain delay differential equations with V-jump