RELIABILITY ANALYSIS OF THE UNCERTAIN FRACTIONAL-ORDER DYNAMIC SYSTEM
WITH STATE CONSTRAINT
Abstract
Uncertain fractional-order differential equations driven by Liu process
are of significance to depict the heredity and memory features of
uncertain dynamical systems. This paper primarily investigates the
reliability analysis of the uncertain fractional-order dynamic system
with a state constraint. On the basis of the first-hitting time (FHT), a
novel uncertain fractional-order dynamic system considering a state
constraint is proposed. Secondly, in view of the relation between the
initial state and the required standard, such uncertain fractional-order
dynamic systems are subdivided into four types. The concept of
reliability of proposed uncertain system with a state constraint is
presented innovatively. Corresponding reliability indexes are ulteriorly
formulated via FHT theorems. Lastly, the uncertain fractional-order
dynamic system with a state constraint is applied to different physical
and financial dynamical models. The analytic expression of the
reliability index is 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. A
sensitivity analysis is also illustrated with respect to various
conditions.