Fractional Model Research Articles

Time delayed fractional diabetes mellitus model and consistent numerical algorithm

The diabetes mellitus model (DMM) is explored in this study. Many health issues are caused by this disease. For this reason, the integer order DMM is converted into the time delayed fractional order model by fitting the fractional order Caputo differential operator and delay factor in the model. It is proved that the generalized model has the advantage of a unique solution for every time t. Moreover, every solution of the system is positive and bounded. Two equilibrium states of the fractional model are worked out i.e. disease free equilibrium state and the endemic equilibrium state. The risk factor indicator, R0 is computed for the system. The stability analysis is carried out for the underlying system at both the equilibrium states. The key role of R0 is investigated for the disease dynamics and stability of the system. The hybridized finite difference numerical method is formulated for obtaining the numerical solutions of the delayed fractional DMM. The physical features of the numerical method are examined. Simulated graphs are presented to assess the biological behavior of the numerical method. Lastly, the outcomes of the study are furnished in the conclusion section.

Modeling Ebola Dynamics with a Φ-Piecewise Hybrid Fractional Derivative Approach

Ebola virus disease (EVD) is a severe and often fatal illness posing significant public health challenges. This study investigates EVD transmission dynamics using a novel fractional mathematical model with five distinct compartments: individuals with low susceptibility (S1), individuals with high susceptibility (S2), infected individuals (I), exposed individuals (E), and recovered individuals (R). To capture the complex dynamics of EVD, we employ a Φ-piecewise hybrid fractional derivative approach. We investigate the crossover effect and its impact on disease dynamics by dividing the study interval into two subintervals and utilize the Φ-Caputo derivative in the first interval and the Φ-ABC derivative in the second interval. The study determines the basic reproduction number R0, analyzes the stability of the disease-free equilibrium and investigates the sensitivity of the parameters to understand how variations affect the system’s behavior and outcomes. Numerical simulations support the model and demonstrate consistent results with the theoretical analysis, highlighting the importance of fractional calculus in modeling infectious diseases. This research provides valuable information for developing effective control strategies to combat EVD.

Forecasting Carbon Dioxide Emission Regional Difference in China by Damping Fractional Grey Model

The emission of carbon dioxide is the main reason for many global warming problems. Although China has made tremendous efforts to reduce carbon emission, the space–time dynamics of the carbon emission trend is still imbalanced. To forecast CDED in China, the Dagum Gini coefficient was applied to measure regional CDED. Then, a grey correlation model was used to select potential influence factors and a wrapping method for selecting the optimal subset. DGMC is proposed to forecast CDED. The research results showed that the DGMC generalization performance is significantly superior to other models. The MAPE of DGMC in six cases are 1.18%, 1.11%, 0.66%, 1.13%, 1.27% and 0.51%, respectively. The RMSPEPR of DGMC in six cases are 1.08%, 1.21%, 0.97%, 1.36%, 1.41% and 0.57%, respectively. The RMSPEPO of DGMC in six cases are 1.29%, 0.69%, 0.02%, 0.58%, 0.78% and 0.32%, respectively. In future trends, the eastern carbon dioxide emission intraregional differences will decrease. Additionally, the intraregional differences in western and middle-region carbon dioxide emissions will expand. Interregional carbon emission difference will display a narrowing trend. Compared with the traditional grey model and ANN model, integrating the influence factor information significantly improved forecasting accuracy. The proposed model will present better balanced historical information and accurately forecast future trends. Finally, policy recommendations are proposed based on the research results.

European vulnerable options pricing under sub-mixed fractional jump-diffusion model with stochastic interest rate

With the development of financial markets, the trading of financial derivatives has become more flexible. To meet the demands of investors, over-the-counter (OTC) trading of options has also become increasingly frequent, raising concerns about accurately pricing vulnerable options. This study investigates the pricing problem of European vulnerable options under the sub-mixed fractional jump-diffusion (SMFJ) model. Firstly, the underlying asset price model and the counterparty company value model are established under the SMFJ model with a sub-mixed fractional Vasicek stochastic interest rate. Then, analytical solutions for the European vulnerable options are obtained using the quasi-martingale measure transformation and the risk-neutral pricing method. Additionally, the accuracy of the pricing formula is verified through the Monte Carlo simulation method. Finally, the rationality and validity of the established model are confirmed by numerical simulations, and the influence of key parameters on the pricing models is analyzed.

A fractional order SIR model describing hesitancy to the COVID-19 vaccination

This study introduces a SIR (Susceptible-Infectious-Recovered) model using fractional derivatives to assess the population's hesitancy to the COVID-19 vaccination campaign in Portugal. Leveraging the framework developed by Angstmann [1], our approach incorporates fractional derivatives to best describe the nuanced dynamics of the vaccination process. We begin by examining the qualitative properties of the proposed model. To substantiate the inclusion of fractional derivatives, empirical data along with statistical criteria are applied. Numerical simulations are performed to compare both integer and fractional order models. An epidemiological interpretation for the fractional order of the model is provided, in the context of a vaccination campaign.

Experimental and numerical analysis of the vibrational behaviour of metallic structures filled with damping materials

This work focuses on characterizing and modeling the vibrational behavior of hollow metallic structures filled with damping material. Vibration tests are first carried on a hollow structure, then two filling materials are considered: a cast viscoelastic material and a granular material composed of epoxy and polyurethane beads. Modal parameters (natural frequencies, modal damping and mode shapes) are extracted from the Frequency Response Functions with experimental modal analysis tools. Damping ratios greater than 5~\% are measured. Given the difference in the nature of the filling materials, dissipation mechanisms are different. The effectiveness of a damping material depends on the type of structural modes (bending, torsion or wall mode) to be damped, and dissipation in filling materials cannot be modelled by a constant loss factor or viscous damping. Consequently, a finite element modeling of the structure filled with viscoelastic material is proposed. Numerical modal parameters of the structure are correlated with experimental measurements. By extension, a bead mix material law, based on a fractional Zener model, is proposed, whose parameters are obtained by inverse identification.

Fractional order modeling of ecological and epidemiological systems: ambiguities and challenges

Fractional order modeling of ecological and epidemiological systems: ambiguities and challenges

Fetal Fraction of Cell-Free DNA in the Prediction of Adverse Pregnancy Outcomes: A Nationwide Retrospective Cohort Study.

To assess the added value of fetal fraction of cell-free DNA in the maternal circulation in the prediction of adverse pregnancy outcomes. Retrospective cohort study. Nationwide implementation study on non-invasive prenatal testing (NIPT; TRIDENT-2 study). Pregnant women in the Netherlands opting for NIPT between June 2018 and June 2019. Two logistic regression prediction models were constructed for each adverse pregnancy outcome. The first model (base model) included prognostic clinical parameters that were selected from existing first-trimester prediction models for adverse pregnancy outcomes. The second model (fetal fraction model) included fetal fraction as a predictor on top of the prognostic clinical parameters included in the base model. The added prognostic value of fetal fraction was assessed by comparing the base and fetal fraction models in terms of goodness of fit and predictive performance. Likelihood ratio test (LRT), area under the curve (AUC) and Integrated Discrimination Improvement (IDI) index. The study cohort consisted of 56 110 pregnancies. The incidence of adverse pregnancy outcomes was 5.7% for hypertensive disorders of pregnancy (HDP; n = 3207), 10.2% for birthweight < p10 (n = 5726), 3.2% for birthweight < p2.3 (n = 1796), 3.4% for spontaneous preterm birth (sPTB; n = 1891), 3.4% for diabetes (n = 1902) and 1.3% for congenital anomalies (n = 741). Adding fetal fraction to the base model improved model fit for HDP, birthweight < p10, birthweight < p2.3, all sPTB, and diabetes, but not for congenital anomalies (LRT p < 0.05). For HDP, the AUC improved from 0.67 to 0.68 by adding fetal fraction to the base model (p = 0.14) with an IDI of 0.0018 (p < 0.0001). For birthweight < p10, the AUC improved from 0.65 to 0.66 (p < 0.0001) with an IDI of 0.0023 (p < 0.0001). For birthweight < p2.3, the AUC improved from 0.67 to 0.69 (p < 0.0001) with an IDI of 0.0011 (p < 0.0001). For all sPTB, the AUC was similar for both models (AUC 0.63, p = 0.021) with an IDI of 0.00028 (p = 0.0023). For diabetes, the AUC was similar (AUC 0.72, p = 0.35) with an IDI of 0.00055 (p = 0.00015). Fetal fraction has statistically significant but limited prognostic value in the prediction of adverse pregnancy outcomes in addition to known prognostic clinical parameters.

Heat transfer analysis of Walter’s-B flow over a vertical plate by using fractional operator

The present study deals with the unsteady Walter’s-B fluid with hybrid fractional derivative namely constant proportional Caputo type with singular kernel. In this paper, we find new analytical solutions of a well-known problem of the fluid dynamics known as Stokes’ first problem. Using dimensional variables governing equations convert into dimensionless form. To solve the model analytically, one uses the Laplace transform approach. Analytical and numerical evaluations of the inverse Laplace transform have been conducted. The influence of several embedded flow properties, including the magnetic parameter, Grashof number, dimensionless time, Prandtl number, Schmidt number, and fractional parameter is analyzed graphically. More specifically, compared to the classical model, the fractional model provides a wider range of integral curves and better represents the flow behavior. The temperature and velocity of the fluid decrease with increasing fractional parameters during short intervals of time, but exhibit the reverse pattern over longer durations. Skin friction, the Sherwood number, and the Nusselt number are numerical quantities linked to engineering that are statistically computed and provided in tabular form.

Sliding mode control design using a generalized reduced-order fractional model for chemical processes

This article presents a comprehensive study that evaluates the potential advantages of adopting a unified, systematic, and organized general fractional model within the Sliding Mode Control (SMC) design framework. The exploration extends to the model's applicability in a variety of disciplines. Although prior research has utilized SMC and fractional-order systems independently, no previous work has established a mathematical framework that integrates a generic fractional-order SMC model. The study addresses this gap and highlights potential implications for control design and applications in a variety of fields, particularly for chemical processes.

Primary care payment models and avoidable hospitalizations in Ontario, Canada: A multivalued treatment effects analysis.

Improving access to primary care physicians' services may help reduce hospitalizations due to Ambulatory Care Sensitive Conditions (ACSCs). Ontario, Canada's most populous province, introduced blended payment models for primary care physicians in the early- to mid-2000s to increase access to primary care, preventive care, and better chronic disease management. We study the impact of payment models on avoidable hospitalizations due to two incentivized ACSCs (diabetes and congestive heart failure) and two non-incentivized ACSCs (angina and asthma). The data for our study came from health administrative data on practicing primary care physicians in Ontario between 2006 and 2015. We employ a two-stage estimation strategy on a balanced panel of 3710 primary care physicians (1158 blended-fee-for-service (FFS), 1388 blended-capitation models, and 1164 interprofessional team-based practices). First, we account for the differences in physician practices using a generalized propensity score based on a multinomial logit regression model, corresponding to three primary care payment models. Second, we use fractional regression models to estimate the average treatment effects on the treated outcome (i.e., avoidable hospitalizations). The capitation-based model sometimes increases avoidable hospitalizations due to angina (by 7 per 100,000 patients) and congestive heart failure (40 per 100,000) relative to the blended-FFS-based model. Switching capitation physicians into interprofessional teams mitigates this effect, reducing avoidable hospitalizations from congestive heart failure by 30 per 100,000 patients and suggesting better access to primary care and chronic disease management in team-based practices.

Existence and Uniqueness Solution for a Mathematical Model with Mittag-Leffler Kernel

In this work, we analyse the fractional order West Nile Virus model involving the Atangana-Baleanu derivatives. Existence and uniqueness solutions were obtained by the fixed-point theorem. Another impressive aspect of the work is illustrated by simulations of different fractional orders by calculating the numerical solutions of the mathematical model.

Technological and financial development as drivers of Latin America's energy transition

Transitioning to clean energy is a challenge for Latin American countries whose socio-economic realities require economic development and environmental sustainability to be carefully balanced. To drive this energy transition, it is essential that funding and technological innovation align with local contexts. This study aims to assess the implementation of the energy transition in Latin America from 2015 to 2020. To do this a performance indicator is developed that uses Data Envelopment Analysis (DEA) and employs data on areas such as patents and financial development as inputs. Subsequently, a Fractional Regression Model (FRM) is used to explore the socio-economic factors influencing this performance and examine its determinants. The results demonstrate significant variations in energy transition outcomes across the sample, with Brazil and Peru consistently achieving maximum DEA scores. Financial development was found to attract capital for the energy transition, with Brazil leading in the Financial Markets Development Index during the period studied. High population density was found to negatively impact energy transition across all FRM model specifications. Negative correlations between gross fixed capital formation and the level of energy transition suggest that there is lower investment in renewable energy in countries with less efficient transitions. Additionally, investment in R&D was only positively and statistically significant in efficient countries.

Isolating financial cycles using the fractional cyclical model in selected economies: 1970–2019

We attempt in this paper to identify financial cycles in 43 countries using data from 1970 to 2019. We use a model based on stochastic cycles that employ fractional integration. The results indicate that the average duration of the cycles is 23 years for Denmark, India, South Korea, Sweden, Spain, Switzerland, and the United States. Our study contributes to the field of research by proposing an alternative model and method for researching financial cycles. The advantage of using such an approach is the ability to isolate more robust stochastic cycles allowing for the possibility of the existence of multiple financial cycles in financial data. It is also found that the credit-GDP ratio exhibits long memory and persistent behavior at the long run frequency. Long memory is found in a number of countries at the cyclical structure with shock of the dynamics of the financial cycle lasting long before disappearing in some of the countries examined.

Tailoring porosity: Unveiling the ideal alumina support (aerogel, xerogel, cryogel) for high-performance CO2 capture with polyethylene glycol

This study investigates enhancing CO2 capture through high polyethylene glycol (PEG) loading on alumina aerogel (Al2O3-A), comparing it with alumina cryogel (Al2O3-C) and xerogel (Al2O3-X). Focusing on sustainable carbon capture and storage (CCS), the research optimizes PEG’s CO2 adsorption by adjusting the porosity of these alumina supports. Key characterization techniques, including XRD, FESEM, FTIR, and N2 adsorption-desorption analysis, were utilized. The study evaluated the effects of pressure, temperature, and PEG loading on CO2 capture capacity using response surface methodology (RSM). Optimal conditions (25 °C, 9.0 bar, 61.0 % PEG) achieved a CO2 adsorption capacity of 443 mg/g. The Hill model was most effective in describing the CO2 adsorption, while the fractional order model accurately depicted the kinetics. Thermodynamic analysis confirmed that the adsorption process is spontaneous, exothermic, and physical. The results underscore the potential of PEG/Al2O3-A for effective CO2 capture, highlighting its high stability, capacity, and reusability, and advancing sustainable carbon capture technologies.

What Determines the Adoption of Conservation Agriculture? Evidence from Quebec.

Conservation agriculture (CA) is promoted by various organisations and scholars as alternative to conventional agriculture to meet growing food demand with minimal damage on environment; but its factors of adoption have not been well identified. The study uses the recent composite index of adoption of CA developed by Takam Fongang et al. (2023) to analyse the factors of adoption of conservation agriculture among maize and soybean farmers in Quebec. Using data from 93 maize and soybean producers and a Fractional logit model, the study shows that adoption of CA increases with farmer's favourable perceptions of yield and easiness of implementing CA, off-farm employment and higher education. The study therefore indicates that higher education, technical assistance and popularisation of performance of CA can play a significant role in boosting adoption of CA in Quebec.

Synchronization on fractional multiplex higher-order networks.

This paper explores the synchronization problem in fractional multiplex higher-order networks. Initially, a fractional multiplex higher-order network model is established, which seamlessly integrates multiplex structures with higher-order interactions. Subsequently, by leveraging a well-crafted Lyapunov function, the Lyapunov direct method, and fractional inequalities, it is demonstrated that the fractional multiplex higher-order network can achieve intra-layer synchronization, inter-layer synchronization, and complete synchronization. Finally, the theoretical findings are validated through two numerical examples featuring a simplicial complex or hypergraph structures within the intra-layer network.

Analyzing creep-recovery behavior of tropical Entandrophragma cylindricum wood: Traditional and fractional modeling methods

Analyzing creep-recovery behavior of tropical Entandrophragma cylindricum wood: Traditional and fractional modeling methods

A Comparative Study of Cave System Calcium Isotope Ratios: Implications for Quantitative Reconstruction of Paleorainfall From Speleothems

AbstractVariations in speleothem calcium isotope ratios (δ44Ca) are thought to be uniquely controlled by prior carbonate precipitation (PCP) above a drip site and, when calibrated with modern data, show promise as a semi‐quantitative proxy for paleorainfall. However, few monitoring studies have focused on δ44Ca in modern cave systems. We present a multi‐year comparative study of δ44Ca, carbon isotopes (δ13C), and trace elemental ratios from cave drip waters, modern calcite, and host rocks from two cave systems in California—White Moon Cave (WMC) and Lake Shasta Caverns (LSC). Drip water and calcite δ44Ca from both caves indicate PCP‐driven enrichment, and we used a simple Rayleigh fractionation model to quantify PCP variability over the monitoring period. Modern calcite trace element and δ44Ca data positively correlate at WMC, but not at LSC, indicating a shared PCP control on these proxies at WMC but not at LSC. At both WMC and LSC, we observe an inverse relationship between PCP and rainfall amounts, though this relationship is variable across individual drip sites. Our modeled data suggest that WMC experiences ∼20% more PCP than LSC, consistent with the fact that WMC receives less annual rainfall. This work supports speleothem δ44Ca as an independent constraint on PCP that can aid in the interpretation of other hydrologically sensitive proxies and provide quantitative estimates of paleorainfall. Additional, long‐term monitoring studies from a variety of climate settings will be key for understanding δ44Ca variability in cave systems more fully and better constraining the relationship between PCP and rainfall.

Two Numerical Approaches for Solving Fractional Model of Chemical Kinetics Problem via Chebyshev Polynomials

Two Numerical Approaches for Solving Fractional Model of Chemical Kinetics Problem via Chebyshev Polynomials