Fractional-order Model Research Articles

Fractional calculus integration for improved ECG modeling: A McSharry model expansion

This study introduces a new method for modeling electrocardiogram (ECG)11- CR: Compression Ratio; FDE: Fractional Differential Equation; GA: Genetic Algorithm; IDE: Integer Differential Equation; MAE: Mean Absolute Error; MSE: Mean Square Error; NRMSE: Normalized Root Mean Square Error; PC: Predictor Corrector; PRD: Percentage Root Mean Square Difference; QS: Quality Score; RMSE: Root Mean Square Error waveforms using Fractional Differential Equations (FDEs). By incorporating fractional calculus into the well-established McSharry model, the proposed approach achieves improved representation and high precision for a wide range of ECG waveforms. The research focuses on the impact of integrating fractional derivatives into Integer Differential Equation (IDE) models, enhancing the fidelity of ECG signal modeling.To optimize the model's unknown parameters, a combination of the Predictor-Corrector method for solving FDEs and genetic algorithms for optimization is utilized. The effectiveness of the fractional-order model is assessed through distortion metrics, providing a comprehensive evaluation of the modeling quality.Comparisons show that the fractional-order model outperforms the traditional McSharry IDE model in modeling quality and compression efficiency. It improves modeling quality by 48.40 % in MSE and compression efficiency by 23.18 % when applied on five beat types of MIT/BIH arrhythmia database. The fractional-order model demonstrates enhanced flexibility while preserving essential McSharry model characteristics, with fractional orders (α) ranging from 0.96 to 0.99 across five beat types.

HIV/AIDS control owing to local and global awareness, diagnosis, treatment tactics and control theory: fractional order modeling

HIV/AIDS control owing to local and global awareness, diagnosis, treatment tactics and control theory: fractional order modeling

Fractional-order modeling and nonlinear dynamics analysis of voltage mode controlled flyback converter

Fractional-order modeling and nonlinear dynamics analysis of voltage mode controlled flyback converter

High performance computational approach to study model describing reversible two-step enzymatic reaction with time fractional derivative

Enzyme reactions have numerous applications in diverse disciplines of science like chemistry, biology and biomechanics. In this study, we examine the role and act of enzymes in chemical reactions which is considered in the frame of fractional order model. The proposed model includes system of four equations which are studied via Caputo fractional operator. The systems of non-linear equations are evaluated by a semi-analytical approach called q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q$$\\end{document}-homotopy analysis transform method. The uniqueness and existence of the solutions has been investigated through fixed point theorem. The solutions of the proposed model are achieved through the considered method and the obtained outcomes are in the form of series which shows rapid convergence. The solutions are computed and graphs are plotted for the obtained results using mathematica software. The achieved results by the proposed method are unique and illustrate the significant dynamics of the considered model via 3D plots and graphs. The results of this study demonstrate the importance and effectiveness of projected derivative and technique in the analysis of time dependent fractional mathematical models. This study also gives an idea to extend the applications of enzymatic reactions in drug development, bio mechanics, and chemical reactions in various cellular metabolisms. Also, enzymatic reactions have a vital role in the fields of the food industry for processing food, in biotechnology for the manufacture of biofuels, and in metabolic engineering to design metabolic pathways.

Fractional-Order Modeling and Identification for an SCR Denitrification Process

This paper presents an application of a fractional-order system on modeling an industrial process system with large inertia and time delay. The traditional integer-order model of the process system is extended to a fractional-order one in this work. To identify the parameters of the proposed fractional-order model, an output-error identification algorithm is presented. Based on the experimental step response data of the selective catalytic reduction (SCR) denitrification process in a power plant, this proposed fractional-order model shows a better fitting result compared with the typical integer-order models. An integer-order proportional–integral (PI) controller is designed for the process plant using a simple scheme according to the identified fractional-order and integer-order models, respectively. Validation tests are performed based on the obtained fractional-order and integer-order models, demonstrating the advantages of the proposed fractional-order model with the corresponding system identification approach for industrial processes with large inertia and time delay.

Design and Comparison of Fractional-Order Controllers in Flotation Cell Banks and Flotation Columns Used in Copper Extraction Processes

This work explores efficiency improvements in the copper flotation stage, a complex nonlinear, multivariable process subject to numerous perturbations. The primary objective is to design a fractional-order PID (FOPID) control strategy and a fractional-order model reference adaptive control (FOMRAC) system. The parameters for these controllers are optimized using the particle swarm optimization (PSO) algorithm with an objective function tailored to the control goals. This study employs models of both a bank series of five flotation cells and a flotation column. Their performance results are compared against traditional controllers, such as an integer-order PID and MRAC. The findings reveal that fractional-order controllers offer notable advantages over their integer-order counterparts, showing improved performance metrics with minimal changes to the existing control framework. This research highlights the effectiveness of fractional control in enhancing flotation processes and introduces a novel application of fractional control techniques in this area.

A new fractional-order model for defining the dynamics of ending student strikes at a university

A new fractional-order model for defining the dynamics of ending student strikes at a university

Fractional Model for Blood Flow in a Stenosed Artery Under MHD Effect Through a Porous Medium

This paper presents a fractional approach as a substitute to the integer-order model, describing the magnetohydrodynamics (MHD) effect of blood flow in a stenosed artery. We not only obtain an analytical solution for the fractional governing equation but also present an expression for the wall-shear stress. After the successful verification of our model with established models, we carry out a two-step validation with the experimental data existing in literature. Then, we analyze the obtained plots by using the analytic expression. We exhibit how fractional model (FM) is helpful for controlling the blood flow through a stenosed artery. This study also indicates that magnetic field intensity significantly controls the flow velocity and wall-shear stress to a great extent. We also show that the external magnetic field, along with the fractional order of the governing equation, plays a pivotal role in the solution of the problem involving the treatment of stenosis. Finally, we conduct some experimental data approximation by the solution to establish the credibility of the proposed fractional-order model.

Sustainable application of modified Luffa cylindrica biomass for removal of trimethoprim in water by adsorption with process optimization.

The present study describes a set of methodological procedures (seldom applied together), including (i) development of an alternative adsorbent derived from abundant low-cost plant biomass; (ii) use of simple low-cost biomass modification techniques based on physical processing and chemical activation; (iii) design of experiments (DoE) applied to optimize the removal of a pharmaceutical contaminant from water; (iv) at environmentally relevant concentrations, (v) that due to initial low concentrations required determination by ultra-performance liquid phase chromatography coupled to mass spectrometry (UPLC-MS/MS). A central composite rotational design (CCRD) was employed to investigate the performance of vegetable sponge biomass (Luffa cylindrica), physically processed (crushing and sieving) and chemically activated with phosphoric acid, in the adsorption of the antibiotic trimethoprim (TMP) from water. The optimized model identified pH as the most significant variable, with maximum drug removal (91.1 ± 5.7%) achieved at pH 7.5, a temperature of 22.5°C, and an adsorbent/adsorbate ratio of 18.6mgµg-1. The adsorption mechanisms and surface properties of the adsorbent were examined through characterization techniques such as scanning electron microscopy (SEM), point of zero charge (pHpzc) measurement, thermogravimetric analysis (TGA), specific surface area, and Fourier-transform infrared spectroscopy (FTIR). The best kinetic fit was obtained by the Avrami fractional-order model. The hypothesis of a hybrid behavior of the adsorbent was suggested by the equilibrium results presented by the Langmuir and Freundlich models and reinforced by the Redlich-Peterson model, which achieved the best fit (R2 = 0.982). The thermodynamic study indicated an exothermic, spontaneous, and favorable process. The maximum adsorption capacity of the material was 2.32 × 102µgg-1 at an equilibrium time of 120min. Finally, a sustainable and promising adsorbent for the polishing of aqueous matrices contaminated by contaminants of emerging concern (CECs) at environmentally relevant concentrations is available for future investigations.

State of Charge Estimation of Lithium-Ion Batteries Based on Fractional-Order Model with Mul-ti-Innovations Dual Cubature Kalman Filter Method

An accurate estimation of the lithium battery’s state of charge (SOC) is critical. The article proposes a dual fractional order multi-innovations cubature Kalman filter (DFOMICKF) algorithm for estimating lithium battery SOC. The algorithm adopts the idea of multiple time scales, where one of the FOMICKF is used to identify the circuit model parameters online in the macro time scale. Another FOMICKF is used to estimate the SOC in the micro time scale, and the circuit parameters updated online in real-time are passed into the estimation of the SOC filter to form an online joint estimation method of SOC and circuit parameters. Finally, multiple algorithms of DFOMICKF, FOMICKF, FOCKF, and CKF are compared and experimented under different working conditions to compare and analyze the estimated SOC errors. It is verified that the proposed algorithm can solve the problems of inaccuracy, poor convergence, and poor robustness of the traditional Kalman filtering algorithm for estimating SOC, which has good research value.

Global Dynamics and Optimal Control of a Fractional-Order SIV Epidemic Model with Nonmonotonic Occurrence Rate

This paper performs a detailed analysis and explores optimal control strategies for a fractional-order SIV epidemic model, incorporating a nonmonotonic incidence rate. In this paper, the population of vaccinated individuals is included in the disease dynamics model. After proving the non-negative boundedness of the fractional-order SIV model, we focus on analyzing the equilibrium point characteristics of the model, delving into its existence, uniqueness, and stability analysis. In addition, our research includes formulating optimal control strategies specifically aimed at minimizing the number of infections while keeping costs as low as possible. To validate the theoretical findings and uncover the practical efficacy and prospects of control measures in mitigating epidemic spread, numerical simulations are performed.

SOC estimation of adaptive untraceable Kalman filtered lithium batteries based on fractional order modeling

SOC estimation of adaptive untraceable Kalman filtered lithium batteries based on fractional order modeling

A new approximation solutions for Fractional Order Biological Population Model

The homotopy permutation approach is used in this article to solve the fractional-order biological population model (FOBPM). The fractional derivative is defined using the Atangana-Baleanu operator (ABO). The suggested technique provides a number of solutions for FOBPM. The HPM technique is regarded as one of the finest analytical processes for solving fractional-order, nonlinear PDEs, notably the FOBPM, since it requires less computations and has a greater rate of convergence than other analytical approaches.

Dynamical behavior of a fractional-order epidemic model for investigating two fear effect functions

Using the Caputo operator, a model for a fractional-order epidemic is developed to investigate the fear effect in a pathogenic environment and vaccination procedure. First, we examine if the proposed model is positive. Next, based on the value of the control reproduction number Rc, we compute both the control reproduction and strength numbers and derive the stability criteria of the disease-free equilibrium. In fact, we use the comparison theorem to show that the disease-free equilibrium point is globally asymptotically stable whenever Rc<1. Next, we prove that the solutions of the fractional model exist and are unique. Finally, several numerical simulations are conducted to verify our theoretical results.

Fractional-order burgers model for coral concrete creep

With the rapid development of marine engineering construction, coral aggregate has been widely applied in practical engineering. Its creep characteristics must be emphasized, but only a few experimental studies have been conducted, and theoretical research has not yet been reported. In this study, based on the traditional Burgers rheological model and using the fractional order software components Able dashpot, constructs a fractional order creep model for coral concrete and provides a calculation method. Comparison shows that the traditional Burgers rheological model cannot adjust the creep rate and development degree in calculations, resulting in a large deviation between its predicted results and experimental values. However, the fractional order model established in this paper aligns with the creep development law of coral concrete, and its calculated values match well with experimental values, making it suitable for predicting the creep characteristics of coral concrete under different water-cement ratios. Sensitivity analysis of the fractional order can achieve effective control over the prediction of creep development in coral concrete in practical engineering. The fractional order creep model established in this paper can provide a basis for predicting and evaluating the long-term performance of coral concrete in practical engineering.

On nonlinear dynamical analysis of a fractional-order two-strains Nipah virus model

The Nipah virus (NiV) is one of the most lethal viruses which can infect humans and lead to fatal encephalitis. The recent significant awareness of NiV is due to its elevated death rate and effective transmission capabilities among humans. With its recurrent outbreaks and exceptionally high mortality rate, the NiV infections have emerged as one of the most concerning hazards to public health. The exploration of NiV and its characteristics revealed that NiV has two distinct strains, namely, the Malaysia (NiVM) strain and the Bangladesh (NiVB) strain. In this paper, we propose a novel Caputo fractional order mathematical model to simulate the dynamics of the two strains NiV. The positivity and boundedness of the model’s solutions are investigated. The existence and asymptotic stability of the equilibrium points of the model are examined. The analysis of basic reproduction number is presented to determine whether the infection will die out or persist. The effects of key parameters of the model on its dynamical behaviors are also explored. Finally, efficient numerical technique is used to confirm the analytical results through detailed numerical simulations.

LVIM Approach to Analyse the Fractional Order Model for Childhood Diseases

LVIM Approach to Analyse the Fractional Order Model for Childhood Diseases

Synthesis of Highly Porous Lignin-Sulfonate Sulfur-Doped Carbon for Efficient Adsorption of Sodium Diclofenac and Synthetic Effluents.

Herein, a novel sulfur-doped carbon material has been synthesized via a facile and sustainable single-step pyrolysis method using lignin-sulfonate (LS), a by-product of the sulfite pulping process, as a novel carbon precursor and zinc chloride as a chemical activator. The sulfur doping process had a remarkable impact on the LS-sulfur carbon structure. Moreover, it was found that sulfur doping also had an important impact on sodium diclofenac removal from aqueous solutions due to the introduction of S-functionalities on the carbon material's surface. The doping process effectively increased the carbon specific surface area (SSA), i.e., 1758 m2 g-1 for the sulfur-doped and 753 m2 g-1 for the non-doped carbon. The sulfur-doped carbon exhibited more sulfur states/functionalities than the non-doped, highlighting the successful chemical modification of the material. As a result, the adsorptive performance of the sulfur-doped carbon was remarkably improved. Diclofenac adsorption experiments indicated that the kinetics was better described by the Avrami fractional order model, while the equilibrium studies indicated that the Liu model gave the best fit. The kinetics was much faster for the sulfur-doped carbon, and the maximum adsorption capacity was 301.6 mg g-1 for non-doped and 473.8 mg g-1 for the sulfur-doped carbon. The overall adsorption seems to be a contribution of multiple mechanisms, such as pore filling and electrostatic interaction. When tested to treat lab-made effluents, the samples presented excellent performance.

Design and analysis of discrete fractional-order chaotic map with offset-boosting behavior

Fractional calculus, as a more accurate tool for depicting the dynamics of complex systems, has been introduced into discrete chaotic maps. To further describe the offset-boosting behavior in discrete systems, a discrete fractional-order chaotic map (DFOCM) based on the Caputo difference operator is constructed. The mapping order of this fractional-order model controls the stability of the fixed point, thereby affecting the dynamic behavior of the map. The dynamics of DFOCM is studied using numerical simulation methods such as bifurcation diagrams and maximum Lyapunov exponents, revealing the presence of multistability. By comparing with integer-order map, it is found that DFOCM exhibit a larger chaotic region. Based on this, the difference between fractional order and integer order offset-boosting behavior is theoretically derived. Specifically, the offset-boosting behavior of fractional-order maps concerning mapping parameters is related to the initial state, which was further demonstrated through numerical simulations. SE complexity proves that the chaotic sequences generated by DFOCM have high unpredictability and pseudo-randomness. Finally, the proposed DFOCM is implemented on the DSP hardware platform, and the physical feasibility of numerical simulation is verified.

Cluster synchronization of fractional-order coupled genetic regulatory networks via pinning control

Cell-to-cell interaction and quorum sensing are universal in real life and have an extremely important biological significance. Besides, fractional-order calculus has tremendous advantages in describing the memory of neurons and the inheritance of genes. In this article, the cluster synchronization of fractional-order coupled genetic regulatory networks (GRNs) is explored by applying pinning control technique. First of all, a type of coupled fractional-order models about GRNs is proposed based on the quorum sensing and cluster expression characteristics of genes. Secondly, by designing pinning control strategies and fractional-order inequalities, several sufficient criteria are constructed to reach cluster synchronization. Furthermore, the selection rule of pining nodes is provided to conduct what nodes can be selected to be pinned and how many nodes are pinned to achieve cluster synchronization. In addition, the fractional-order adaptive control strategy is designed to regulate control gains. Several numerical results are provided lastly to confirm the theoretical analysis.