一类分数阶微积分的中值定理及应用

Riemann-Liouville分数阶微积分算子是一类带有一个函数的分数阶微积分算子的特殊情形，以Riemann-Liouville分数阶微积分算子的积分中值定理和微分中值定理为基础，我们得到了一类带有一个函数的分数阶微积分算子的积分中值定理和微分中值定理，并给出其在计算方面的一些应用。     

Effect of microwave heating time on the gel properties of chicken myofibrillar proteins and their formation mechanism

The present work was conducted to illustrate the mechanism of gel formation of myofibrillar proteins (MPs) under different microwave heating times. The results showed that the denaturation enthalpy (ΔH) of the MPs significantly decreased when the heating time increased from 3 to 9 s and then completely disappeared as the heating time progressed, indicating that the MPs gradually denatured and subsequently aggregated with increasing heating time, which was further verified by the changes in the secondary structure, electrophoretic bands, and gel properties (e.g., water holding capacity and textural profiles) of the MPs. Microstructural images indicated that the MP gel formed under 12 s had the most compact network, indicating that extended microwave heating time could induce quality deterioration of MP gels. Moreover, the hydrophobic forces, electrostatic forces, and disulphide bonds of the MPs gradually intensified with increasing microwave heating time, suggesting that both non-covalent and covalent bonds could promote molecular denaturation and subsequent aggregation of MPs. In addition, correlation analysis revealed that the changes in the molecular conformation of MPs induced by different microwave heating times could effectively regulate the formation of MP gels and their related properties.     

Robust adaptive passivity-based PIλD control

In this article, we develop proportional, fractional-integral, and derivative () controllers for the regulation and tracking problems of nonlinear systems. The analytic results are obtained by extending the passivity-based approach to include fractional operators. Robustness under parametric uncertainty is dealt with by a combination with an adaptive scheme. It is also shown their robustness under additive noise and their robustness under uncertainty in the derivation order. The advantages in the controlled system performance and in the control energy consumption in comparison to classic PI and proportional integral derivative controllers are illustrated for the quadratic boost converter and a benchmark system in the literature.     

Preventive replacement policies with time of operations,mission durations,minimal repairs and maintenance triggering approaches

When a mission arrives at a random time and lasts for a duration, it becomes an interesting problem to plan replacement policies according to the health condition and repair history of the operating unit, as the reliability is required at mission time and no replacement can be done preventively during the mission duration. From this viewpoint, this paper proposes that effective replacement policies should be collaborative ones gathering data from time of operations, mission durations, minimal repairs and maintenance triggering approaches. We firstly discuss replacement policies with time of operations and random arrival times of mission durations, model the policies and find optimum replacement times and mission durations to minimize the expected replacement cost rates analytically. Secondly, replacement policies with minimal repairs and mission durations are discussed in a similar analytical way. Furthermore, the maintenance triggering approaches, i.e., replacement first and last, are also considered into respective replacement policies. Numerical examples are illustrated when the arrival time of the mission has a gamma distribution and the failure time of the unit has a Weibull distribution. In addition, simple case illustrations of maintaining the production system in glass factories are given based on the assumed data.     

Contract duration: Barrier or bridge to successful public-private partnerships?

Public-private partnerships (PPPs) are predominantly executed through the use of formal contracts which define the relationship between a public agency and private supplier. As such, a PPP is not a generic contract between buyer and supplier but rather a specific contractual arrangement between a public buyer and private supplier. The contract captures the responsibilities of each party in achieving a specific set of performance objectives. Given budgetary pressures faced by public agencies, there is an increasing need for suppliers to make investments which could reduce future-year costs of meeting contract performance objectives. This research addresses two overarching questions specific to the issue of private, supplier-side investment. First, “how does public agency and private supplier perception of risk influence contract duration?” and second, “how does contract duration influence private investment?” To answer these questions, structured interviews were conducted with those in public agencies and private, supplier firms actively engaged in PPPs. Factors suspected to contribute to the risk position of public and private actors were evaluated. Additionally, linkages between public buyer-private supplier risk position, contract duration and private, supplier-side investment were addressed. Outcomes suggest properly structured long-term contracts may: 1) provide the risk mitigation mechanisms needed for both public and private actors, and 2) facilitate private, supplier-side investment.     

The Investigation of the Fractional-View Dynamics of Helmholtz Equations Within Caputo Operator

It is eminent that partial differential equations are extensively meaningful in physics, mathematics and engineering. Natural phenomena are formulated with partial differential equations and are solved analytically or numerically to interrogate the system’s dynamical behavior. In the present research, mathematical modeling is extended and the modeling solutions Helmholtz equations are discussed in the fractional view of derivatives. First, the Helmholtz equations are presented in Caputo’s fractional derivative. Then Natural transformation, along with the decomposition method, is used to attain the series form solutions of the suggested problems. For justification of the proposed technique, it is applied to several numerical examples. The graphical representation of the solutions shows that the suggested technique is an accurate and effective technique with a high convergence rate than other methods. The less calculation and higher rate of convergence have confirmed the present technique’s reliability and applicability to solve partial differential equations and their systems in a fractional framework.     

Fractional fixed-structure H∞ controller design using Augmented Lagrangian Particle Swarm Optimization with Fractional Order Velocity

The optimization of a fixed-structure controller is in general computationally intractable, posing a challenge to control system engineers. This paper introduces a novel technique for designing such control techniques by formulating it as a nonlinear non-convex constrained problem. A novel PSO algorithm, namely the Augmented Lagrangian Particle Swarm Optimization with Fractional Order Velocity (ALPSOFV), is proposed for improving the convergence rate. The structure of the controller is selectable and, therefore, the Fractional Order Proportional Integral Derivative (FOPID) algorithm is chosen in the scope of the study. The results for three test examples show the good performance of the ALPSOFV.     

Research on the hot surface ignition of hydrogen‐air mixture under different influencing factors

To further reveal the pre‐ignition characteristics of hydrogen internal combustion engine, the effect of hot surface characteristic parameters on the ignition characteristics of hydrogen‐air mixture was investigated in this research. Based on the prototype of the constant volume combustion bomb with an overhead glow plug, the duration from the heating of the hot surface to the combustion of hydrogen‐air mixture, the so‐called heating duration, was firstly researched under different fuel‐air equivalence ratio, initial temperature, initial pressure, hot surface temperature, and hot surface area, and the influence of each factor on the heating duration was analyzed. The results show that the order of the effect of each factor on the hot surface ignition is as follows: hot surface temperature > initial pressure of hydrogen‐air mixture > equivalent ratio > initial temperature of hydrogen‐air mixture > hot surface area. The influence of the hot surface characteristic parameters on the heating duration was further analyzed in detail. On this basis, the relationship among the critical ignition temperature, the heating duration and the hot surface area was researched and established. The results show that the heating duration is the only major factor affecting the critical ignition temperature. Finally, the research results were applied to analysis the pre‐ignition in hydrogen internal combustion engine.     

Determination of supercapacitor parameters based on fractional differential equations

In this paper, we estimate the parameter values of a fractional-order model of supercapacitors involving fractional derivatives of Liouville-Caputo, Caputo-Fabrizio, and Atangana-Baleanu and fractional conformable derivative in the Liouville-Caputo sense. We present the exact solution of the considered model using the properties of the Laplace transform operator together with the convolution theorem. They developed numerical simulations using each one of the fractional derivatives; the results were compared graphically with experimental data obtained from different supercapacitors using standard laboratory equipment. The nonlocal parameters involved in the equivalent electrical circuit for the supercapacitor model are recalculated for each fractional derivative using a particle swarm optimization algorithm for generating optimal solutions.