Reliability analysis of the uncertain fractional‐order dynamic system with state constraint

Abstract

Uncertain fractional‐order differential equations driven by the Liu process are of significance to depict the heredity and memory features of uncertain dynamical systems. This paper primarily analyses the reliability of the uncertain fractional‐order dynamic system with a state constraint. First, consider the possibility that the real dynamical system is actually limited; the state constraint is absorbed to the ordinary uncertain fractional‐order dynamical system. The concept of reliability of uncertain system is presented innovatively, which are ulteriorly formulated through the existing first‐hitting time theorem. Second, based on the proposed reliability and under a given sufficient condition, a novel uncertain fractional‐order dynamic system with a state constraint is modeled mathematically; corresponding minimum operation ability of the uncertain system is also given. Lastly, the uncertain fractional‐order dynamic system with a state constraint is applied to different physical and financial dynamical models. Analytic expressions of reliability indexes are derived to demonstrate the reasonableness of our model. Meanwhile, expected time response and American barrier option prices are calculated by using the predictor–corrector scheme. The sensitivity analysis is also presented for the numerical examples.