Existence and moment estimate for solutions of highly nonlinear fractional stochastic hybrid differential equations

The aim of this paper is to discuss the existence and moment estimate for solutions of highly nonlinear fractional stochastic hybrid differential equations. This hybrid system is characterized under a general framework, including, fractional calculus which is used to study the memory, hereditary and hidden properties of the dynamics of complex systems, and high nonlinearity which is introduced to better meet the needs of practical applications. Different from the currently available literature which assumes the diffusion and drift coefficients to satisfy the linear growth condition, we consider the diffusion and drift coefficients of the underlying hybrid system to satisfy the polynomial growth condition. By making use of the stopping time technique, the truncation function and the general Itô formula, we show the existence, uniqueness and moment estimate of the global solution of the system being considered. In addition, we propose an example to demonstrate the theory of abstract results.