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Uncertain fractional difference equations may preferably describe the behavior of the systems with the memory effect and discrete feature in the uncertain environment. So it is of great significance to investigate their stability. In this paper, the concept of finite-time stability almost surely for uncertain fractional difference equations is introduced. A finite-time stability theorem is then stated by Mittag–Leffler function and proved by a generalized Gronwall inequality on a finite time. Some examples are finally presented to illustrate the validity of our results.

Some complex systems may suffer from failure processes arising from soft failures and hard failures. The existing researches have shown that the reliability of a dynamic system is not constant under uncertain random environments. First, two types of uncertain random optimization models are proposed where reliability index is quantified by chance measure based on whether soft and hard failures are independent or not. It is considered that internal degradation is driven by left Caputo fractional linear difference equation, while shocks are defined as discrete i.i.d. random variables. The shocks may generate additional uncertain degradation shifts when considering the competing dependent failure processes. Then, two proposed optimization reliability problems may be transformed into their equivalent deterministic forms on the basis of [Formula: see text]-path, and improved gradient descent method is applied to obtain optimal solutions. Finally, the numerical example of a micro-engine indicates that the optimization models are beneficial to the reliability of engineering systems.

This paper primarily focuses on LQ optimal control problem of fractional-order discrete-time systems based on uncertainty theory that is a significant tool to model belief degree. First, an equivalent LQ problem, which is integer-order one, is presented by expanding the state variables with the unchanging control variables. This equivalent problem is then solved by dynamic programming approach. Accordingly, the solution of the proposed LQ optimal control problem reduces to solve a system of backward matrix difference equations. Finally, a numerical example is provided to show how to solve the proposed LQ optimal control problem. As an application, an LQ optimal control problem of macroeconomic system is discussed by the achieved results.

In this paper, the finite-time stability in mean for the uncertain fractional order linear time-invariant discrete systems is investigated. First, the uncertain fractional order difference equations with the nabla operators are introduced. Then, some conditions of finite-time stability in mean for the systems driven by the nabla uncertain fractional order difference equations with the fractional order [Formula: see text] are obtained by the property of Riemann–Liouville-type nabla difference and the generalized Gronwall inequality. Furthermore, based on these conditions, the state feedback controllers are designed. Finally, some examples are presented to illustrate the effectiveness of the results.

Uncertain fractional differential equation driven by Liu process plays a significant role in depicting the memory effects of uncertain dynamical systems. This paper mainly investigates the stability problems for the Caputo type of uncertain fractional differential equations with the order [Formula: see text]. The concept of stability in measure of solutions to uncertain fractional differential equation is proposed based on uncertainty theory. Several sufficient conditions for ensuring the stability of the solutions are derived, respectively, in which the systems are divided into two cases with order [Formula: see text] and [Formula: see text]. Some illustrative examples are performed to display the effectiveness of the proposed results.

This paper primarily focuses on the distributions of the solutions for uncertain fractional difference equations by comparison theorems. First, comparison theorems are obtained for the fractional difference equations involving Riemann–Liouville type. Then the concepts of symmetrical uncertain variable and α -path to an uncertain fractional difference equation are introduced. Moreover, the relations between the solutions for the uncertain fractional difference equations with symmetrical uncertain variables and their α -paths are established and verified by the obtained comparison theorems. Finally, the numerical results of the uncertainty distributions of solutions for the uncertain fractional difference equations are proposed, considering the relations between their solutions and α -paths.

We evaluated how metabolic disorders affected antihypertension therapy. 2,912 rural Chinese patients with hypertension who provided blood samples, demographic and clinical data at baseline and after 1 year of antihypertension therapy were evaluated. At baseline, 1,515 patients (52.0%) were already receiving drug therapy and 11.4% of them had controlled blood pressure (BP). After 1 year, all 2,912 patients were receiving antihypertension therapy that was administered by community physicians, and 59.42% of them had controlled BP. Central obesity and abnormal triglyceride, high-density lipoprotein cholesterol, and glucose were associated with 15–70% higher risks of uncontrolled hypertension. Metabolic syndrome using the JIS criteria was associated with poor BP control (odds ratio: 1.71 and 1.54 for the baseline and follow-up datasets, respectively). The risk of uncontrolled hypertension increased with the number of metabolic disorders (p for trend