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

Abstract

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.

On the numerical solution of second order delay differential equations via a novel approach

“…DDEs have applications in a large number of real life problems, including immune system [8], dynamics of the population [19], cell proliferation [7], the bistable device [31], control theory [10], etc. Many techniques have been developed to study the solution of DDEs such as in [16], the authors explored the uniqueness and existence of a solution to DDEs. Jafari et al [15], studied the numerical solution of pantograph type DDEs via the transferred Legendre pseudospectral, they also discussed the convergence of the method.…”