Design of Delayed Fractional State Variable Filter for Parameter Estimation of Fractional Nonlinear Models
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AbstractThis paper presents a novel direct parameter estimation method for continuous-time fractional nonlinear models. This is achieved by adapting a filter-based approach that uses the delayed fractional state variable filter for estimating the nonlinear model parameters directly from the measured sampled input–output data. A class of fractional nonlinear ordinary differential equation models is considered, where the nonlinear terms are linear with respect to the parameters. The nonlinear model equations are reformulated such that it allows a linear estimator to be used for estimating the model parameters. The required fractional time derivatives of measured input–output data are computed by a proposed delayed fractional state variable filter. The filter comprises of a cascade of all-pass filters and a fractional Butterworth filter, which forms the core part of the proposed parameter estimation method. The presented approaches for designing the fractional Butterworth filter are the so-called, square root base and compartmental fractional Butterworth design. According to the results, the parameters of the fractional-order nonlinear ordinary differential model converge to the true values and the estimator performs efficiently for the output error noise structure.
CitationAllafi, W., Zajic, I., Uddin, K. et al. Nonlinear Dyn (2018). https://doi.org/10.1007/s11071-018-4519-0
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Antidiabetic activities of chloroform fraction of Anthocleista vogelii Planch root bark in rats with diet- and alloxan-induced obesity-diabetesAnyanwu, Gabriel O.; Iqbal, Jamshed; Khan, Shafi U.; Zaib, Sumera; Rauf, Khalid; Onyeneke, Chukwu E.; Ojo, Opeolu O. (Elsevier, 2018-10-18)ETHNOPHARMACOLOGICAL RELEVANCE: Anthocleista vogelii Planch is a medicinal plant traditionally used in West Africa for the management and treatment of diabetes mellitus. AIM OF THE STUDY: To determine the antidiabetic activities of chloroform fraction (CF) of Anthocleista vogelii Planch root bark in rats with diet- and alloxan-induced obesity-diabetes. MATERIALS AND METHODS: Inhibitory activities of CF against α-amylase and α-glucosidase activities were determined in vitro. Three weeks old rats were fed with high-fat diet for 9 weeks to induce obesity prior to further induction of diabetes using alloxan (150 mg/kg body weight, i.p.). Blood glucose levels and body weight were measured every 7 days throughout the experiment. Glucose tolerance was assessed in normal and CF-treated rats on day 21. Terminal blood samples were collected from sacrificed animals for the measurement of serum insulin levels. Pancreases were excised from treated and untreated animals for histopathological examination. RESULTS: LCMS/MS chromatographic profile of CF via positive and negative modes revealed 13 and 23 compounds respectively. Further analysis revealed quebrachitol (QCT), loganin, sweroside, oleoside 11-methyl ester and ferulic acid, which have been previously reported for their antidiabetic activities, as constituents of CF. CF inhibited activities of α-amylase (IC50 = 51.60 ± 0.92 µg/ml) and α-glucosidase (IC50 = 5.86 ± 0.97 µg/ml) in a dose-dependent manner. Treatment of animals with obesity-diabetes with 100 and 200 mg/kg CF significantly improved glucose tolerance (P < 0.001) and enhanced serum insulin levels (P < 0.05) compared to diabetic control rats. CONCLUSIONS: Antidiabetic activities of CF might be mediated via inhibition of α-amylase and α-glucosidase activities, elevation of serum insulin concentration, and enhancement of insulin and leptin sensitivity in obesity-diabetes rats. This study further substantiates the traditional use of A. vogelii in the management and treatment of diabetes in Africa and encourages further studies to investigate its mechanism of action.