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The nabla fractional-order uncertain difference equation with Caputo-type was analyzed in this article. To begin, the existence and uniqueness theorem of solutions for nabla Caputo uncertain difference equations with almost surely bounded uncertain variables was presented. Furthermore, the uncertainty distributions of the solutions for the proposed equations were obtained by establishing a connection between the solutions of equations and their α-paths based on new comparison theorems. Finally, an application of the uncertain difference equations in a logistic population model involving Allee effect was provided and examples were performed to demonstrate the validity of the theoretical results presented.

Abstract To model complex systems with discrete-time features and memory effects in the uncertain environment, a definition of an uncertain fractional forward difference equation with Riemann–Liouville-like forward difference is introduced. Moreover, analytic solutions to a type of special linear uncertain fractional difference equations are presented by the Picard iteration method. Then, an existence and uniqueness theorem of the solutions is proved by applying Banach contraction mapping theorem. Finally, two examples are provided to illustrate the validity of the existence and uniqueness theorem.

Abstract 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