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。     

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.     

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.     

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.     

Stumped nature hyperjerk system with fractional order and exponential nonlinearity: Analog simulation,bifurcation analysis and cryptographic applications

This article presents the construction and consumption of hyperjerk system having chaotic nature with the commensurate ordered fractional derivative on rapidly digitalized emerging technologies. The system analyzed analytically using Lipschitz condition and numerically with the help of predictor corrector approaches. Originality of constructed system is confirmed using log error plots which gives satisfactory small values on finite time scale. The dynamical performances of the complex system are termed in multiple phase planes by the mean of their significant nature. Stability and bifurcation analysis around the fractional derivative is also studies for the various parameter of system to check the visibility of chaotic solution. The system is also designed in analog circuit simulator with the aid of operational amplifier, anti-parallel semiconductor diodes for validation of the system. With the help of random number generators (RNGs), binary array generated from the hyperjerk system and plugged in to the NIST 800–22 test suite to measure the randomness. The array having high randomness is used as strong cypher key for the cryptographic execution straightforwardly in both direction encryption and decryption.     

Validating the moderating role of age in multi-perspective acceptance model of wearable healthcare technology

The recent trend of aging population, not to mention the unprecedented pandemic, draws great attention from the general public about health concerns. Since healthcare information technology is different from non-healthcare information technology, additional contexts should be properly incorporated into technology acceptance research to accurately identify influential factors affecting the acceptance of wearable healthcare technology. Thus, we selectively reconfigured factors from health, privacy, and socio-demographic contexts to formulate a health-aware acceptance model. Then, it was empirically analyzed using structural equation modeling. Based on the results, whereas privacy concerns were directly associated with intention to use wearable healthcare technology, health concerns were not. Moreover, age had a moderating effect on social influence and facilitating conditions. These findings suggest valuable insights that the adoption rate of healthcare technology is increased by 1) keeping personal information securely, 2) facilitating social interaction among users, and 3) offering intuitive user experience for elderly people.     

Patterning a π-conjugated polyelectrolyte through sequential polymerization of a bifunctional ionic liquid monomer

An electronically conductive polyelectrolyte is prepared by the sequential polymerization of a bifunctional imidazolium-based ionic liquid (IL) monomer, composed of a thienyl and vinyl containing cation paired with a tetrafluoroborate anion. In the first step, potentiodynamic electropolymerization of the thienyl moiety forms a cationic polyalkylthiophene that is soluble in select organic solvents. Cyclic voltammetry (CV) was used to determine the polymer p-doping potential (0.31 V) and the bipolaronic state (1.49 V). The polymer exhibits electrochromism, converting from red in the neutral state (λ_max = 443 nm) to dark blue in the polaronic state (λ_max = 819 nm). The solution-processable polymer can be cast into a film, masked and patterned by UV-initiated free radical polymerization of the vinyl moiety. Small-angle X-ray scattering (SAXS) revealed that the insoluble crosslinked polyalkylthiophene–polyvinylimidazolium adopts a lamellar structure with a lattice spacing of 3.3 nm. Four-probe d.c. conductivity measurements determined the de-doped electrical conductivity was 1.0 × 10⁻² S/cm. The results underscore the importance of the anion in controlling the polymerization of IL monomers.     

Variational design of open cross-section thin-walled beam under stability constraints

A thin-walled beam is in pure bending subjected to couples M₀. The open cross-section profile has two ribs, with cross-section A₀ and it is shaped symmetrically towards the plane perpendicular to the bending plane. The ribs are located at the profile ends. The shape of the profile line is searched for. Criterion is the minimal value of the cross-section area A₁ of the beam. The problem is described by means of variational calculus. Within the numerical calculations a Runge–Kutta method is used. The optimal shapes of beam profiles are shown graphically.     

双亲性聚合物调理剂在护发素中的应用研究

研究了双亲性聚合物作为调理剂成分在无硅油护发素中的应用。以溶液自由基聚合法合成了双亲性无规聚合物聚(苯乙烯-co-丙烯酸)。利用阳离子表面活性剂山嵛基三甲基氯化铵与聚合物之间的阳离子-π电子作用,将双亲性无规共聚物聚(苯乙烯-co-丙烯酸)吸附到头发表面起到顺滑作用。通过调节聚合物中苯环与山嵛基三甲基氯化铵的摩尔比、山嵛基三甲基氯化铵的浓度以及使用量,制备具有优异梳理性能的护发素,对护发素效果进行评价,并与含硅护发素进行比较。结果表明:最优条件下,双亲性聚合物在头发上的残留量为102μg/g头发;在护发素中添加双亲聚合物后能够显著改善湿梳理性能,其湿梳性优于市售含硅护发素;经护发素处理后的头发毛鳞片规整、无翘起,且双亲聚合物在头发上无累积效应。