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。     

基于小波变换的分数阶微分算法在肝脏肿瘤CT图像纹理增强中的应用

图像纹理增强过程中容易丢失平滑区域纹理细节，而分数阶微分增强虽然能够非线性保留平滑区域纹理细节，但对频率分辨率敏感。针对这个问题，提出一种基于小波变换的分数阶微分纹理增强算法，应用于平扫计算机断层扫描（CT）图像的肝脏肿瘤区域的纹理增强。首先，通过小波变换将图像感兴趣区分解成多个子带分量；其次，基于分数阶微分定义构造一个带补偿参数的分数阶微分掩膜；最后，使用该掩膜与每个高频子带分量进行卷积并利用小波逆变换重组图像感兴趣区。实验结果表明，该方法在使用较大分数阶次显著增强肿瘤区域的高频轮廓信息的同时，有效地保留了低频平滑的纹理细节：增强后的肝细胞癌区域与原区域相比，信息熵平均增加36.56%，平均梯度平均增加321.56%，平均绝对差值平均为9.287；增强后的肝血管瘤区域与原区域相比，信息熵平均增加48.77%，平均梯度平均增加511.26%，平均绝对差值平均为14.097。     

一类Hilfer型分数阶微分方程解的存在和唯一性

用Banach不动点定理和上下解方法研究了α(1<α <2)阶数和β(0≤β ≤1)类型Hilfer分数阶微分方程的解,给出了方程解的存在和唯一性,并通过例证验证了本文所得结果的有效性.     

Assessing smoke toxicity of burning combustibles by four expressions for fractional effective dose

Toxicity of smoke generated in a fire is difficult to measure accurately. That is because gas sensors for measuring rapidly varying concentrations of toxic gases are not yet developed. Simple expressions are searched for quick measurement in assessing smoke toxicity practically. Four equations on calculating fractional effective dose (FED) related to toxic effluents were reported in the literature, each based on different assumptions. FED value was proposed to be calculated based on peak carbon monoxide concentration and peak carbon dioxide concentration, and transient carbon monoxide, carbon dioxide, and oxygen concentrations. The four values were compared in this article using literature data on toxic gases from different materials measured by (i) cone calorimeter; (ii) full-scale burning tests; and (iii) tunnel full-scale tests. Measured carbon monoxide, carbon dioxide, and oxygen concentrations by standard equipment of oxygen consumption calorimeters were used to calculate the four FED values. It is found that the values of FED based on peak carbon monoxide and carbon dioxide concentrations (denoted as FED₂) are similar to the average values of FED calculated from the updated equation in the literature using the oxygen consumption calorimeters. Putting the values of FED₂ in fire safety design guides is then recommended.     

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.     

Unsteady free convection of second‐grade nanofluid with a new time‐space fractional heat conduction

The Caputo and Caputo–Fabrizio derivative are applied to study a second‐grade nanofluid over a vertical plate. A comparative analysis is presented to study the unsteady free convection of a second‐grade nanofluid with a new time–space fractional heat conduction. The governing equations with mixed time–space fractional derivatives are non‐dimensionalized and solved numerically, and a comparison between the Caputo and the Caputo–Fabrizio models is made. It is found that the temperature is higher for the Caputo–Fabrizio fractional model than the Caputo model, but the higher velocity only exists near the vertical plate for the Caputo–Fabrizio model than the Caputo model. Moreover, the velocity for the Caputo model will exceed the Caputo–Fabrizio model as y evolves.     

并联有源滤波器的改进重复控制策略研究

针对三相整流负载产生的6k±1次谐波,提出静止坐标系下的改进型6k±1重复控制策略。同时将比例控制与改进型重复控制相结合,设计改进重复控制并联比例的复合控制结构。为减小改进重复控制中延时环节不为整数的影响,采用基于Lagrange插值近似的FIR滤波器逼近分数延时特性。最后对系统进行稳定性分析和详细设计方法进行推导。通过Matlab仿真验证改进重复控制策略能有效跟踪6k±1次谐波且具有良好的补偿效果,动态响应较快。     

超分子作用阻尼材料的动态力学模型修正

为提高飞机起落架载荷实测精度，以支柱式起落架结构为研究对象，探讨处理其载荷标定数据的工程方法。首先，对实际受载情况和单向加载工况标定数据的分析，挖掘出三向载荷、缓冲支柱压缩行程与应变码值间的数学关系，将预测的数学关系代入到多向工况的标定数据中，验证了它们的准确性;其次，根据两种标定数据回归方法，提出了对应使用的支柱式起落架载荷-应变标定方程的数学模型;最后，将两种标定方程代回到标定数据中，计算起落架三向载荷，所有反算载荷的误差均在可控范围内，表明标定方程满足精度要求。将标定方程代入实测数据中，实测曲线符合变化规律。该处理方法的应用能有力提高支柱式起落架的起飞-着陆载荷实测和载荷谱编制的准确度。     

An efficient numerical scheme for solving fractional infinite-horizon optimal control problems

This paper presents an efficient numerical method to solve fractional infinite-horizon optimal control problems, where the dynamic control system depends on Caputo fractional derivatives. First, by a suitable change of variable, we transform the fractional infinite-horizon optimal control problem to a finite-horizon one. Then, with the help of an approximation, we replace the Caputo derivative to integer order derivative. According to the Pontryagin minimum principle (PMP) for optimal control problems and by constructing an error function, we define an unconstrained minimization problem. In the optimization problem, we use trial solutions for state, costate and control functions where these trial solutions are constructed by using two-layered perceptron neural network. Some numerical results are introduced to explain our main results.