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Recently, a new formulation has been introduced for non-local mechanics in terms of fractional calculus. Fractional calculus is a branch of mathematical analysis that studies the differential operators of an arbitrary (real or complex) order and is used successfully in various fields such as mathematics, science and engineering. The purpose of this paper is to introduce a new fractional non-local theory which may be applicable in various simple or complex mechanical problems.

In this paper (by using fractional calculus), a fractional non-local theory based on the conformable fractional derivative (CFD) definition is presented, which is a generalized form of the Eringen non-local theory (ENT). The theory contains two free parameters: the fractional parameter which controls the stress gradient order in the constitutive relation and could be an integer and a non-integer and the non-local parameter to consider the small-scale effect in the micron and the sub-micron scales. The non-linear governing equation is solved by the Galerkin and the parameter expansion methods. The non-linearity of the governing equation is due to the presence of von-Kármán non-linearity and CFD definition.

The theory has been used to study linear and non-linear free vibration of the simply-supported (S-S) and the clamped-free (C-F) nano beams and then the influence of the fractional and the non-local parameters has been shown on the linear and non-linear frequency ratio.

A new parameter of the theory (the fractional parameter) makes the modeling more fixable – this model can conclude all of integer and non-integer operators and is not limited to special operators such as ENT. In other words, it allows us to use more sophisticated mathematics to model physical phenomena. On the other hand, in the comparison of classic fractional non-local theory, the theory applicable in various simple or complex mechanical problems may be used because of simpler forms of the governing equation owing to the use of CFD definition.

Creep behavior of concrete at high temperature has become a major concern in building structures, such as factories, bridges, tunnels, airports and nuclear buildings. Therefore, a simple and accurate prediction model for the high-temperature creep behavior of concrete is crucial in engineering applications.

In this paper, the variable-order fractional operator is introduced to capture the high-temperature creep behavior of concrete. By assuming that the variable-order function is a linear function with time, the proposed model benefits from the advantages of both formal simplicity and the physical significance for macroscopic intermediate materials. The effectiveness of the model is demonstrated by data fitting with existing experimental results of high-temperature creep of two representative concretes.

The results show that the proposed model fits well with the experimental data, and the value of order is increasing with the increase of the applied stress levels, which meets the fact that higher stress can accelerate the rate of creep. Furthermore, the relationship between the model parameters and loading conditions is deeply analyzed. It is found that the material coefficients are constant at a constant temperature, while the order function parameters are determined by the applied stress levels. Finally, the variable-order fractional model can be further written into a general equation of time and applied stress.

This paper provides a simple and practical variable-order fractional model for predicting the creep behavior of concrete at high temperature.

The purpose of this study is to provide some references about applying the semi-active particle damper to enhance the stability of the pipe structure.

This paper establishes the dynamical models of semi-active particle damper based on traditional dynamical theory and fractional-order theory, respectively. The semi-active particle damping vibration isolation system applied in a pipe structure is proposed, and its analytical solution compared with G-L numerical solution is solved by the averaging method. The quantitative relationships of fractional-order parameters (a and kp) are confirmed and their influences on the amplitude-frequency response of the vibration isolation system are analyzed. A fixed point can be obtained from the amplitude-frequency response curve, and the optimal parameter used for improving the vibration reduction effect of semi-active particle damper can be calculated based on this point. The nonlinear phenomenon caused by nonlinear oscillators is also investigated.

The results show that the nonlinear stiffness parameter p will cause the jump phenomenon while p is close to 87; with the variation of nonlinear damping parameter μ, the pitchfork bifurcation phenomenon will occur with an unstable branch after the transient response; with the change of fractional-order coefficient k_p, a segmented bifurcation phenomenon will happen, where an interval that k_p between 18.5 and 21.5 has no bifurcation phenomenon.

This study establishes a mathematical model of the typical semi-active particle damping vibration isolation system according to fractional-order theory and researches its nonlinear characteristics.

This paper aims to characterize the relationship between the interelectrode capacitance (C) of metal-oxide-semiconductor field-effect transistors (MOSFETs) and the applied bias voltage (V) by a fractional-order equivalent model.

A Riemann–Liouville-type fractional-order equivalent model is proposed for the C–V characteristic of MOSFETs, which is based on the mathematical relationship between fractional calculus and the semiconductor physical model for the interelectrode capacitance of metal oxide semiconductor structure. The C–V characteristic data of an N-channel MOSFET are obtained by Silvaco TCAD simulation. A differential evolution-based offline scheme is exploited for the parameter identification of the proposed model.

According to the results of theoretical analysis, mathematical derivation, simulation and comparison, this paper illustrates that, along with the variation of bias voltage applied, the interelectrode capacitance (C) of MOSFETs performs a fractional-order characteristic.

This work uncovers the fractional-order characteristic of MOSFETs’ interelectrode capacitance. By the proposed model, the influence of doping concentration on the gate leakage parasitic capacitance of MOSFETs can be revealed. In the pre-defined doping concentration range, the relative error of the proposed model is less than 5% for the description of C–V characteristics of metal-oxide-semiconductor field-effect transistors (MOSFETs). Compared to some existing models, the proposed model has advantages in both model accuracy and model complexity, and the variation of model parameters can directly reflect the relationship between the characteristics of MOSFETs and the doping concentration of materials. Accordingly, the proposed model can be used for the microcosmic mechanism analysis of MOSFETs. The results of the analysis produce evidence for the widespread existence of fractional-order characteristics in the physical world.

This paper aims to focus on the accurate analysis of the fractional heat transfer in a two-dimensional (2D) rectangular monolayer tissue with three different kinds of lateral boundary conditions and the quantitative evaluation of the degree of thermal damage and burn depth.

A symplectic method is used to analytically solve the fractional heat transfer dual equation in the frequency domain (s-domain). Explicit expressions of the dual vector can be constructed by superposing the symplectic eigensolutions. The solution procedure is rigorously rational without any trial functions. And the accurate predictions of temperature and heat flux in the time domain (t-domain) are derived through numerical inverse Laplace transform.

Comparison study shows that the maximum relative error is less than 0.16%, which verifies the accuracy and effectiveness of the proposed method. The results indicate that the model and heat source parameters have a significant effect on temperature and thermal damage. The pulse duration (Δt) of the laser heat source can effectively control the time to reach the peak temperature and the peak slope of the thermal damage curve. The burn depth is closely correlated with exposure temperature and duration. And there exists the delayed effect of fractional order on burn depth.

A symplectic approach is presented for the thermal analysis of 2D fractional heat transfer. A unified time-fractional heat transfer model is proposed to describe the anomalous thermal behavior of biological tissue. New findings might provide guidance for temperature prediction and thermal damage assessment of biological tissues during hyperthermia.

This study aims to compare the performance of the conventional and fractional order proportional-integral-derivative (PID and FOPID) controllers tuned with a particle swarm optimization (PSO) and genetic algorithm (GA) for quadrotor control.

In this study, the gains of the controllers were tuned using PSO and GA, which are included in the heuristic optimization methods. The tuning processes of the controller’s gains were formulated as optimization problems. While generating the objective functions (cost functions), four different decision criteria were considered separately: integrated summation error (ISE), integrated absolute error, integrated time absolute error and integrated time summation error (ITSE).

According to the simulation results and comparison tables that were created, FOPID controllers tuned with PSO performed better performances than PID controllers. In addition, the ITSE criterion returned better results in control of all axes except for altitude control when compared to the other cost functions. In the control of altitude with the PID controller, the ISE criterion showed better performance.

While a conventional PID controller has three parameters (Kp, Ki, Kd) that need to be tuned, FOPID controllers have two additional parameters (µ). The inclusion of these two extra parameters means more flexibility in the controller design but much more complexity for parameter tuning. This study reveals the potential and effectiveness of PSO and GA in tuning the controller despite the increased number of parameters and complexity.

The purpose of this offered research is to articulate a multifaceted kind of highly unstable initial perturbation and further analyze the performance of the plasma particles for time-fractional order evaluation.

For this purpose, the authors designed specific geometry and further interpreted it into the mathematical model using the concepts of the Vlasov Maxwell system. The suggested algorithm is based on the finite-difference and spectral estimation philosophy. The management of time and memory in generic code for computational purposes is also discussed.

The main purpose is to analyze the fractional behavior of plasma particles and also the capability of the suggested numerical algorithm. Due to initial perturbations, there are a lot of sudden variations that occurred in the formulated system. Graphical behavior shows that SR parameter produces devastation as compared to others. The variation of fractional parameter between the defend domain demonstrates the hidden pictures of plasma particles. The design scheme is efficient, convergent and has the capability to cover the better physics of the problem.

Plasma material is commonly used in different areas of science. Therefore, in this paper, the authors increase the capability of the mathematical plasma model with specific geometry, and further suitable numerical algorithm is suggested with detailed physical analysis of the outcomes. The authors gave a new direction to study the performance of plasma particles under the influence of LASER light.

In the recent era, science has produced a lot of advancements to study and analyze the physical natural process, which exist everywhere in the real word. On behalf of this current developments, it is now insufficient to study the first-order time evaluation of the plasma particles. One needs to be more precise and should move toward the bottomless state of it, that is, macroscopic and microscopic time-evaluation scales, and it is not wrong to say that there exits a huge gap, to study the time evaluation in this discussed manner. The presented study is entirely an advanced and efficient way to investigate the problem into the new directions. The capability of the proposed algorithm and model with fractional concepts can fascinate the reader to extend to the other dimensions.

This study aims to analyse the conditional volatility of the Vietnam Index (Ho Chi Minh City) and the Hanoi Exchange Index (Hanoi) with a specific focus on their application to risk management tools such as Expected Shortfall (ES).

First, the author tests both indices for long memory in their returns and squared returns. Second, the author applies several generalised autoregressive conditional heteroskedasticity (GARCH) models to account for asymmetry and long memory effects in conditional volatility. Finally, the author back tests the GARCH models’ forecasts for Value-at-Risk (VaR) and ES.

The author does not find long memory in returns, but does find long memory in the squared returns. The results suggest differences in both indices for the asymmetric impact of negative and positive news on volatility and the persistence of shocks (long memory). Long memory models perform best when estimating risk measures for both series.

Short-time horizons to estimate the variance should be avoided. A combination of long memory GARCH models with skewed Student’s t-distribution is recommended to forecast VaR and ES.

Up to now, no analysis has examined asymmetry and long memory effects jointly. Moreover, studies on Vietnamese stock market volatility do not take ES into consideration. This study attempts to overcome this gap. The author contributes by offering more insight into the Vietnamese stock market properties and shows the necessity of considering ES in risk management. The findings of this study are important to domestic and foreign practitioners, particularly for risk management, as well as banks and researchers investigating international markets.

Apart from the well-known, high persistence of daily financial volatility data, there is also a short correlation structure that reverts to the mean in less than a month. We find this short correlation time scale in six different daily financial time series and use it to improve the short-term forecasts from generalized auto-regressive conditional heteroskedasticity (GARCH) models. We study different generalizations of GARCH that allow for several time scales. On our holding sample, none of the considered models can fully exploit the information contained in the short scale. Wavelet analysis shows a correlation between fluctuations on long and on short scales. Models accounting for this correlation as well as long-memory models for absolute returns appear to be promising.

The aim of the study was to show that a new method, using a look-up table technique, can be used to detect the presence and position of an inclusion embedded in a tissue-like material. Due to the time-consuming nature of the finite element (FE) method or FEM, real-time applications involving FEM as part of a control loop, are traditionally limited to slowly varying systems. By using a simplified two-dimensional FE model and a look-up table, we show by simulations and experiments that it is possible to achieve reasonable computational times in a tactile resonance sensor application.

A piezoelectric disk was placed in the center of a silicone rubber disk (SRD) with viscoelastic properties, where it acted as both sensor and actuator and dissipated radial acoustic waves into the silicone. The look-up table was constructed by calculating the radial Lamb wave transition frequencies in the impedance frequency response of the sensor while varying the position of an inclusion. A position-matching algorithm was developed that matched measured and calculated Lamb wave transitions and thereby identified the presence and position of an inclusion.

In an experiment, the position of a hard inclusion was determined by measuring the Lamb transition frequencies of the first radial resonance in two SRDs. The result of the matching algorithm for Disk 1 was that the matched position was less than 3% from the expected value. For Disk 2, the matching algorithm erroneously reported two false positions before reporting a position that was less than 5% from the expected value. An explanation for this discrepancy is presented. In a verifying experiment, the algorithm identified the condition with no inclusion present.

The approach outlined in this work, adds to the prospect of developing time-sensitive diagnostic instruments. This approach has the potential to provide a powerful technique to quickly present spatial information on detected tumors.