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.     

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.     

Comparing the expressiveness of downward fragments of the relation algebra with transitive closure on trees

Motivated by the continuing interest in the tree data model, we study the expressive power of downward navigational query languages on trees and chains. Basic navigational queries are built from the identity relation and edge relations using composition and union. We study the effects on relative expressiveness when we add transitive closure, projections, coprojections, intersection, and difference; this for Boolean queries and path queries on labeled and unlabeled structures. In all cases, we present the complete Hasse diagram. In particular, we establish, for each query language fragment that we study on trees, whether it is closed under difference and intersection.     

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.     

Fractional observer to estimate periodical forces

In the present work we propose a fractional state observer with constant gain to estimate the periodical force exerted on a mechanical system by measuring only its displacement. The state observer is designed from both the Fourier series that approximates the periodical force and the equations of the damped harmonic oscillator that represents the behavior of the system. Specifically, the reconstruction of the force is carried out from the estimates of the series coefficients, which in fact are part of the dynamical system that composes the observer. Adams-Bashforth-Moulton method is used to compute the fractional derivatives of the observer in the Liouville-Caputo sense. Experiments based on real data are presented to show the advantages of using a fractional observer in the reconstruction of forces.     

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。     

定位误差的微分计算法

介绍了在夹具设计中应用高等数学微分近似计算原理计算定位误差的方法和实例 ,从而简化了较为复杂定位误差的分析和计算。     

A fractional-spectral method for vibration of damped space structures

Based on the theory of fractional calculus and the spectral theory of vibration, a new spectrally formulated finite element method of analysis is developed which is capable of making accurate predictions of the dynamic response of structures with added dampers. The frequency-dependence damping characteristic of structural materials can be modelled accurately using the fractional derivative model. It is shown that the proposed method can be extended to develop a nonlinear damping element which can be used to model structural dampers. The approach has an advantage over the usual viscous treatment, which appears to lack physical motivation. The nonlinear damping solution is shown graphically, and the consistency of method is investigated. Using a computer program, the proposed formulation has been used to derive the dynamic response of a tall structure with added viscoelastic dampers.     

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.