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We propose a biodynamic model for managing waterborne diseases over an Internet of Things (IoT) network, leveraging the scalability of LoRa IoT technology to accommodate a growing human population. The model, based on fractional order derivatives (FOD), enables smart prediction and control of pathogens that cause waterborne diseases using IoT infrastructure. The human-pathogen-based biodynamic FOD model utilises epidemic parameters (SVIRT: susceptibility, vaccination, infection, recovery, and treatment) transmitted over the IoT network to predict pathogenic contamination in water reservoirs and dumpsites in Iji-Nike, Enugu, the study community in Nigeria. These pathogens contribute to person-to-person, water-to-person, and dumpsite-to-person transmission of disease vectors. Five control measures are proposed: potable water supply, treatment, vaccination, adequate sanitation, and health education campaigns. A stable disease-free equilibrium point is found when the effective reproduction number of the pathogens, R0eff<1 and unstable if R0eff>1. While other studies showed a 98.2% reduction in infections when using IoT alone, this paper demonstrates that combining the SVIRT epidemic control parameters (such as potable water supply and health education campaign) with IoT achieves a 99.89% reduction in infected human populations and a 99.56% reduction in pathogen populations in water reservoirs. Furthermore, integrating treatment with sanitation results in a 99.97% reduction in infected populations. Finally, combining these five control strategies nearly eliminates infection and pathogen populations, demonstrating the effectiveness of multifaceted approaches in public health and environmental management. This study provides a blueprint for governments to plan sustainable smart cities for a growing population, ensuring potable water free from pathogenic contamination,in line with the United Nations Sustainable Development Goals #6 (Clean Water and Sanitation) and #11 (Sustainable Cities and Communities).

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Calcium ions are the second messenger playing as regulators for various cellular activities. Its spatiotemporal control is critical for various brain functions, including neuroplasticity, apoptosis, and cell death. The Endoplasmic Reticulum (ER) plays an important role in determining these spatiotemporal calcium dynamics. Stromal interaction molecule (STIM) - Orai channel on the membrane generates additional calcium flow, whereas other membrane fluxes contribute to cytosolic flux. Due to their anomalous character, we used the Caputo fractional differential operator to mimic these interactions in polar coordinates. Solutions were generated using hybrid integral transform methods to control the analytical approach. Using Green's function yielded a closed-form solution for Mittag-Leffler-type functions. This work emphasizes the significant relationship between calcium and various buffer levels in neurons. The differential transition simulation of a time derivative with space across different parameters indicated a decrease in calcium concentration. Anomalously low buffer levels exhibited the impact of Alzheimer's disease on calcium higher concentration, leading to the death of neurons. Additionally, the research introduces a method involving S100B, BAPTA, and calmodulin buffers to uphold optimal calcium levels within the neuronal cytosol. The applicability of this model with different buffer properties and parameters and memory impacts the calcium concentration with the neurological disorder.

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Calcium plays a crucial role as a second messenger in neuronal signal transduction pathways. The influx of calcium ions through various physicochemical gating channels activates neuronal calcium signaling. The Endoplasmic Reticulum (ER) is a significant intracellular structure that sequesters calcium and controls signaling through SERCA, IPR, and leak channel mechanisms. Disruption of calcium dynamics can trigger intrinsic dyshomeostasis, cell damage, and apoptosis. The present study articulates a Caputo fractional time derivative in the polar coordinate dimensions to investigate the role of nonlocal calcium-free ions in the neuron through the Orai channel, and ER fluxes, incorporating various physiological parameters. The solution was obtained through the hybrid integral transform technique for analytical form. The closed form was generated using Green's function in terms of Mainardi and Wright's functions. Our simulation uncovered the calcium concentration bandwidth of interaction with different neuronal parameters. Parameters and calcium ion synergy show normal and Alzheimer's disease-impacted interaction through different illustrations. Our simulation reveals that S100B and BAPTA have significant calcium-controlling behavior.

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BACKGROUND AND OBJECTIVE: Hepatitis virus infections are affecting millions of people worldwide, causing death, disability, and considerable expenditure. Chronic infection with hepatitis C virus (HCV) can cause severe public health problems because of their high prevalence and poor long-term clinical outcomes. Thus a fractional-order epidemic model of the hepatitis C virus involving partial immunity under the influence of memory effect to know the transmission patterns and prevalence of HCV infection is studied. Investigating the transmission dynamics of HCV makes the issue more interesting. The HCV epidemic model and worldwide dynamics are examined in this study. Calculate the basic reproduction number for the HCV model using the next-generation matrix technique. We determine the model's global dynamics using reproduction numbers, the Lyapunov functional approach, and the Routh-Hurwitz criterion. The model's reproduction number shows how the disease progresses. METHODS: A fractional differential equation model of HCV infection has been created. Maximum relevant parameters, such as fractional power, HCV transmission rate, reproduction number, etc., influencing the dynamic process, have been incorporated. The model's numerical solutions are obtained using the fractional Adams method. Finally, numerical simulations support the theoretical conclusions, showing the great agreement between the two. RESULTS: In the fractional-order HCV infection model, the memory effect, which is not seen in the classical model, was shown on graphs so that disease dynamics and vector compartments could be seen. We found that the fractional-order HCV infection model has more stages of freedom than regular derivatives. Fractional-order derivations, which may be the best and most reliable, explained bodily approaches better than classical order. CONCLUSION: The current study modeled and analyzed a fractional-order HCV infection model. The current approach results in a much better understanding of HCV transmission in a population, which leads to important insights into its spread and control, such as better treatment dosage for different age groups, identifying the best control measure, improving health, prolonging life, reducing the risk of HCV transmission, and effectively increasing the quality of life of HCV patients. The creation of a fractional-order HCV infection model, which provides a better understanding of HCV transmission dynamics and leads to significant insights for better treatment dosages, identification of optimal control measures, and ultimately improvement of the quality of life for HCV patients, is the study's major outcome.

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Chlorophyll fluorescence (ChlF) parameters offer valuable insights into quantifying energy transfer and allocation at the photosystem level. However, tracking their variation based on reflectance spectral information remains challenging for large-scale remote sensing applications and ecological modeling. Spectral preprocessing methods, such as fractional-order derivatives (FODs), have been demonstrated to have advantages in highlighting spectral features. In this study, we developed and assessed the ability of novel spectral indices derived from FOD spectra and other spectral transformations to retrieve the ChlF parameters of various species and leaf groups. The results obtained showed that the empirical spectral indices were of low reliability in estimating the ChlF parameters. In contrast, the indices developed from low-order FOD spectra demonstrated a significant improvement in estimation. Furthermore, the incorporation of species specificity enhanced the tracking of the non-photochemical quenching (NPQ) of sunlit leaves (R2 = 0.61, r = 0.79, RMSE = 0.15, MAE = 0.13), the fraction of PSII open centers (qL) of shaded leaves (R2 = 0.50, r = 0.71, RMSE = 0.09, MAE = 0.08), and the fluorescence quantum yield (ΦF) of shaded leaves (R2 = 0.71, r = 0.85, RMSE = 0.002, MAE = 0.001). Our study demonstrates the potential of FOD spectra in capturing variations in ChlF parameters. Nevertheless, given the complexity and sensitivity of ChlF parameters, it is prudent to exercise caution when utilizing spectral indices for tracking them.

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Leaf water content (LWC) is a vital indicator of crop growth and development. While visible and near-infrared (VIS-NIR) spectroscopy makes it possible to estimate crop leaf moisture, spectral preprocessing and multiband spectral indices have important significance in the quantitative analysis of LWC. In this work, the fractional order derivative (FOD) was used for leaf spectral processing, and multiband spectral indices were constructed based on the band-optimization algorithm. Eventually, an integrated index, namely, the multiband spectral index (MBSI) and moisture index (MI), is proposed to estimate the LWC in spring wheat around Fu-Kang City, Xinjiang, China. The MBSIs for LWC were calculated from two types of spectral data: raw reflectance (RR) and the spectrum based on FOD. The LWC was estimated by combining machine learning (K-nearest neighbor, KNN; support vector machine, SVM; and artificial neural network, ANN). The results showed that the fractional derivative pretreatment of spectral data enhances the implied information of the spectrum (the maximum correlation coefficient appeared using a 0.8-order differential) and increases the number of sensitive bands, especially in the near-infrared bands (700-1100 nm). The correlations between LWC and the two-band index (RVI1156, 1628 nm), three-band indices (3BI-3(766, 478, 1042 nm), 3BI-4(1129, 1175, 471 nm), 3BI-5(814, 929, 525 nm), 3BI-6(1156, 1214, 802 nm), 3BI-7(929, 851, 446 nm)) based on FOD were higher than that of moisture indices and single-band spectrum, with r of - 0.71**, 0.74**, 0.73**, - 0.72**, 0.75** and - 0.76** for the correlation. The prediction accuracy of the two-band spectral indices (DVI(698, 1274 nm) DVI(698, 1274 nm) DVI(698, 1274 nm)) was higher than that of the moisture spectral index, with R2 of 0.81 and R2 of 0.79 for the calibration and validation, respectively. Due to a large amount of spectral indices, the correlation coefficient method was used to select the characteristic spectral index from full three-band indices. Among twenty seven models, the FWBI-3BI- 0.8 order model performed the best predictive ability (with an R2 of 0.86, RMSE of 2.11%, and RPD of 2.65). These findings confirm that combining spectral index optimization with machine learning is a highly effective method for inverting the leaf water content in spring wheat.

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This work presents a fractional-order Wilson-Cowan model derivation under Caputo's formalism, considering an order of 0 < α ≤ 1 . To that end, we propose memory-dependent response functions and average neuronal excitation functions that permit us to naturally arrive at a fractional-order model that incorporates past dynamics into the description of synaptically coupled neuronal populations' activity. We then shift our focus on a particular example, aiming to analyze the fractional-order dynamics of the disinhibited cortex. This system mimics cortical activity observed during neurological disorders such as epileptic seizures, where an imbalance between excitation and inhibition is present, which allows brain dynamics to transition to a hyperexcited activity state. In the context of the first-order mathematical model, we recover traditional results showing a transition from a low-level activity state to a potentially pathological high-level activity state as an external factor modifies cortical inhibition. On the other hand, under the fractional-order formulation, we establish novel results showing that the system resists such transition as the order is decreased, permitting the possibility of staying in the low-activity state even with increased disinhibition. Furthermore, considering the memory index interpretation of the fractional-order model motivation here developed, our results establish that by increasing the memory index, the system becomes more resistant to transitioning towards the high-level activity state. That is, one possible effect of the memory index is to stabilize neuronal activity. Noticeably, this neuronal stabilizing effect is similar to homeostatic plasticity mechanisms. To summarize our results, we present a two-parameter structural portrait describing the system's dynamics dependent on a proposed disinhibition parameter and the order. We also explore numerical model simulations to validate our results.

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This paper examines the issue of almost periodic quasi-projective synchronization of delayed fractional-order quaternion-valued neural networks. First, using a direct method rather than decomposing the fractional quaternion-valued system into four equivalent fractional real-valued systems, using Banach's fixed point theorem, according to the basic properties of fractional calculus and some inequality methods, we obtain that there is a unique almost periodic solution for this class of neural network with some sufficient conditions. Next, by constructing a suitable Lyapunov functional, using the characteristic of the Mittag-Leffler function and the scaling idea of the inequality, the adequate conditions for the quasi-projective synchronization of the established model are derived, and the upper bound of the systematic error is estimated. Finally, further use Matlab is used to carry out two numerical simulations to prove the results of theoretical analysis.

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The purpose of this article is to investigate the optimal control of nonlinear fractional order chaotic models of diabetes mellitus, human immunodeficiency virus, migraine and Parkinson's diseases using genetic algorithms and particle swarm optimization. Mathematical chaotic models of nonlinear fractional order type of the above diseases were presented. Then optimal control for each of the models and numerical simulation was done using genetic algorithm and particle swarm optimization algorithm. The results of the genetic algorithm method are excellent. All the results obtained for the particle swarm optimization method show that this method is also very successful and the results are very close to the genetic algorithm method. Very low values of MSE and RMSE errors indicate that the simulation is effective and efficient. Also, Lie symmetry was calculated for the proposed models and the results were presented.

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In the current power landscape, renewable energy sources (RESs) have assumed a crucial role in satisfying consumer demand. However, as the deployment of renewables increases, certain challenges arise, including issues with system frequency stability, inertia, and damping reduction. To address these concerns, an innovative approach is suggested in this study. The proposed strategy aims to maintain frequency stability in a diverse-source power system that encompasses two interconnected regions incorporating RESs. The proposed strategy comprises a new multi-degree of freedom FOTID controller known as the MDOF-TIλDµN controller in the secondary control loop (SCL) and optimally controlled fuel cells (OFCL) to enhance the system's stability under the effect of renewable energy (RESs) fluctuations. In this context, the gains of the considered strategy (optimal MDOF-TIλDµN in addition to OFCL) have been picked out by using an innovative optimization approach known as the Capuchin search algorithm (CapSA). The statistical tests are used to examine the efficacy of the considered CapSA compared to those of other optimization strategies utilized in previous studies. Furthermore, the performance of the proposed controller in the SCL is verified by contrasting its performance with that of another suggested controller known as MDOF-PIDN as well as other controllers such as PD-IT, PDµN-IλT, 2DOF-TIλDµN, 3DOF-PIDN, 3DOF-TIDN, and 3DOF-PIλDµN. Additionally, grid nonlinearities, including Boiler Dynamics, Generation Rate Constraint, Governor Dead Band, and random communication time delay (CTD), are considered. Moreover, the proposed strategy's performance is verified in the face of system constraints and nonlinearities. Different scenarios are implemented, and the simulation outcomes emphasize the superior performance of the suggested strategy. Therefore, the suggested strategy provides consistent power system adoption wherever it is implemented.

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OBJECTIVES: A new modified Pan-Tompkins' (mPT) method for fetal heart rate detection is presented. The mPT method is based on the hypothesis that optimal fractional order derivative and optimal window width of the moving average filter would enable efficient estimation of fetal heart rate from surface abdominal electrophysiological recordings with relatively low signal-to-noise ratios. METHODS: The algorithm is tested on signals recorded from the abdomen of pregnant women available from the PhysioNet Computing in Cardiology Challenge database. Fetal heart rate detection is performed on 10-s long segments selected by the estimation of signal-to-noise ratios (the extravagance of the fetal QRS peak to its surroundings and to the whole signal; and the mean ratio of fetal and maternal QRS peaks) and on the manually selected segments. RESULTS: The best results are obtained via criteria based on the extravagance of the fetal QRS peak to its surroundings that reached average sensitivity of 97%, positive predictive value of 97%, error rate of ∼3.5%, and F1 score of 97%. The obtained averaged optimal parameters for mPT are 0.51 for fractional order and 24.5 ms for the window width of the moving average filter. CONCLUSION: Proposed mPT algorithm showed satisfactory performance for fetal heart rate detection. Further adaptations of the presented mPT method could be used for peak detection in noisy environments in biomedical signal analysis in general.

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Temperature-frequency sweep tests were performed on silicone rubber to investigate the dynamic viscoelastic properties. The test results show that the viscoelasticity of silicone rubber presents significant temperature dependence and frequency dependence. The dynamic viscoelastic test curves at different temperatures can be shifted along the logarithmic frequency coordinate axis to construct smooth master curves at the reference temperature of 20 °C, covering a frequency range of 10 decades, which indicates thermorheological simplicity on a macro level and frequency temperature equivalence of the silicone rubber material in the experimental temperature range. The van Gurp-Palmen plot and Cole-Cole plot for the test data at various temperatures merge into a common curve, which further validates thermorheological simplicity. The temperature dependent shift factors of silicone rubber material were well characterized by the Williams-Landel-Ferry equation. Moreover, the fractional-order differential Kelvin (FDK) model, the fractional-order differential Zener (FDZ) model, and the improved fractional-order differential Zener (iFDZ) model were used to model the asymmetric loss factor master curve. The result shows that the iFDZ model is in good agreement with the test results, indicating that this model is suitable for describing the asymmetry of dynamic viscoelastic properties of silicone rubber.

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Soil organic matter (SOM) is a crucial indicator of soil fertility. Field hyperspectral reflectance and laboratory SOM data of soil samples from the Yinchuan Plain were used to explore the performance of models based on fractional derivative combined with different spectral indices. Following reciprocal and logarithmic transformation, the reflectance data were processed using fractional derivative from 0 to 2 orders (interval 0.20). Then, the difference index (DI), ratio index (RI), brightness index (BI), normalized difference index (NDI), renormalized difference index (RDI), and generalized difference index (GDI) were constructed. The two-dimensional correlation between the six indices and SOM content were analyzed. The optimal spectral indices were selected to establish SOM estimation models with principal component regression (PCR), partial least square regression (PLSR), back propagation neural network (BPNN), support vector machine (SVM), and geographically weighted regression (GWR). Results showed that the maximum absolute correlation coefficient (MACC) values between DI, RI, NDI, BI, GDI, RDI, and SOM contents increased firstly and then decreased, with the highest values observed at 1.0, 0.6, 1.4, and 1.6 orders. The 0.2-2.0 order RDI under fractional derivative variation could be used for subsequent model construction, in which the optimal combinations of bands for MACC values were mainly concentrated at 400-600 nm and 1300-1700 nm. Among the different models based on the single spectral index RDI, the model based on SVM achieved the highest estimation accuracy, whose modeling determination coefficient, verification determination coefficient and relative percentage difference reached 0.86, 0.87 and 2.32. Our results would provide a scientific reference for quick and accurate SOM assessment and mapping in areas with relatively low SOM content.

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Segmentation of a road portion from a satellite image is challenging due to its complex background, occlusion, shadows, clouds, and other optical artifacts. One must combine both local and global cues for an accurate and continuous/connected road network extraction. This paper proposes a model using fractional derivative-based weighted skip connections on a densely connected convolutional neural network for road segmentation. Weights corresponding to the skip connections are determined using Grunwald-Letnikov fractional derivative. Fractional derivatives being non-local in nature incorporates memory into the system and thereby combine both local and global features. Experiments have been performed on two open source widely used benchmark databases viz. Massachusetts Road database (MRD) and Ottawa Road database (ORD). Both these datasets represent different road topography and network structure including varying road widths and complexities. Result reveals that the proposed system demonstrated better performance than the other state-of-the-art methods by achieving an F1-score of 0.748 and the mIoU of 0.787 at fractional order 0.4 on the MRD and a mIoU of 0.9062 at fractional order 0.5 on the ORD.

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In this paper, we construct the SV1V2EIR model to reveal the impact of two-dose vaccination on COVID-19 by using Caputo fractional derivative. The feasibility region of the proposed model and equilibrium points is derived. The basic reproduction number of the model is derived by using the next-generation matrix method. The local and global stability analysis is performed for both the disease-free and endemic equilibrium states. The present model is validated using real data reported for COVID-19 cumulative cases for the Republic of India from 1 January 2022 to 30 April 2022. Next, we conduct the sensitivity analysis to examine the effects of model parameters that affect the basic reproduction number. The Laplace Adomian decomposition method (LADM) is implemented to obtain an approximate solution. Finally, the graphical results are presented to examine the impact of the first dose of vaccine, the second dose of vaccine, disease transmission rate, and Caputo fractional derivatives to support our theoretical results.

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Solute dispersion is a significant phenomenon during drug targeting to estimate the accumulation of drug particles at the tumour region with the capture efficiency. In this present study, we aim to predict the effective dispersion and saturated concentration of drug carriers during magnetic drug targeting in a microvessel with a time fractional derivative based dispersion model. The magnetic nanoparticles are bound with the non-magnetic materials/microgels with the therapeutic agents to prepare the drug carriers. A magnetic field is created outside the body to control and accelerate the trajectories of the drug carriers. The nature of the blood flow into the vessel is considered as Casson fluid. The velocity of the drug carriers is solved analytically, while the fractional-order dispersion equation is computed numerically using the finite difference technique with the forward time and central space discretization. The influence of fractional-order parameter and model biological parameters such as rheological parameter, permeability parameter related to hydraulic conductivity, magnetization, volume fraction of nanoparticles, tumour-magnet distance, nanoparticle radius, drug elimination, and source term on the relative effective dispersion are discussed. The outcomes showed that both rheological parameters and volume fraction increase drug carrier particle concentration, and that saturating occurs at a later time as they increase. Higher magnetization, permeability parameter related to the hydraulic conductivity, and source term are associated with faster transportation of drug carriers to the tumour site. In addition, we note that by using small particle sizes, a high concentration of the drug-coated nanoparticles will be expected in the tumour area, and this slows the rate at which it reaches the saturation point.

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This study presents a novel approach to investigating COVID-19 and Cholera disease. In this situation, a fractional-order model is created to investigate the COVID-19 and Cholera outbreaks in Congo. The existence, uniqueness, positivity, and boundedness of the solution are studied. The equilibrium points and their stability conditions are achieved. Subsequently, the basic reproduction number (the virus transmission coefficient) is calculated that simply refers to the number of people, to whom an infected person can make infected, as R 0 = 6 . 7442389 e - 10 by using the next generation matrix method. Next, the sensitivity analysis of the parameters is performed according to R 0 . To determine the values of the parameters in the model, the least squares curve fitting method is utilized. A total of 22 parameter values in the model are estimated by using real Cholera data from Congo. Finally, to find out the dynamic behavior of the system, numerical simulations are presented. The outcome of the study indicates that the severity of the Cholera epidemic cases will decrease with the decrease in cases of COVID-19, through the implementation and follow-up of safety measures that have been taken to reduce COVID-19 cases.

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In this paper, we have studied a fractional-order eco-epidemiological model incorporating fear, treatment, and hunting cooperation effects to explore the memory effect in the ecological system through Caputo-type fractional-order derivative. We have studied the behavior of different equilibrium points with the memory effect. The proposed system undergoes through Hopf bifurcation with respect to the memory parameter as the bifurcation parameter. We perform numerical simulations for different values of the memory parameter and some of model parameters. In the numerical results, it appears that the system is exhibiting a stable behavior from a period or chaotic nature with the increase in the memory effect. The system also exhibits two transcritical bifurcations with respect to the growth rate of the prey. At low values of prey's growth, all species go to extinction, at moderate values of prey's growth, only preys (susceptible and infected) can survive, and at higher values of prey's growth, all species survive simultaneously. The paper ended with some recommendations.

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SO42- ion is an important indicator of soil salinization degree, but there are few researches on quantitative inversion of SO42- content based on hyperspectral and fractional-order derivative (FOD). This study aimed to improve the prediction accuracy of SO42- content in arid regions using visible and near-infrared (VIS-NIR) spectroscopy. The study area was divided into three regions according to different human activity stress, namely, lightly affected region (Region A), moderately affected region (Region B) and severely affected region (Region C). The combination estimation method of spectral transformations (R, R, 1/R, lgR, 1/lgR), FOD, significance test band (STB), and partial least squares regression (PLSR) were been constructed, and four models (FULL-PLSR, FOD-FULL-PLSR, IOD-STB-PLSR, FOD-STB-PLSR) were also used to compare and analyze the estimation accuracy. Simulation results show that the optimal prediction model of three regions is FOD-STB-PLSR, its spectral transformation is established by R, 1/R and R in Region A, B, and C, respectively. Its RPD is 2.4701, 3.4679 and 1.9781, and its optimal FOD derivative is located at 1.8-, 1.1- and 1.1-order, respectively. It means that FOD can fully extract VIS-NIR spectroscopy details, the higher-order FOD is more capable of extracting characteristic data than low-order FOD, and the predictive ability of the best estimation model is very good, extremely strong and relatively good in Region A, B and C, respectively. Compared with the best IOD-STB-PLSR of each region, the RPD of the optimal FOD-STB-PLSR model has increased more than 38%, 32%, and 19%, respectively. This study shows that the proposed FOD-STB-PLSR model is suitable for estimating the SO42- ion content of saline soil under different human activity stresses, and the study can provide a certain technical reference value for the monitoring of saline soil in arid areas.

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Many countries worldwide have been affected by the outbreak of the novel coronavirus (COVID-19) that was first reported in China. To understand and forecast the transmission dynamics of this disease, fractional-order derivative-based modeling can be beneficial. We propose in this paper a fractional-order mathematical model to examine the COVID-19 disease outbreak. This model outlines the multiple mechanisms of transmission within the dynamics of infection. The basic reproduction number and the equilibrium points are calculated from the model to assess the transmissibility of the COVID-19. Sensitivity analysis is discussed to explain the significance of the epidemic parameters. The existence and uniqueness of the solution to the proposed model have been proven using the fixed-point theorem and by helping the Arzela-Ascoli theorem. Using the predictor-corrector algorithm, we approximated the solution of the proposed model. The results obtained are represented by using figures that illustrate the behavior of the predicted model classes. Finally, the study of the stability of the numerical method is carried out using some results and primary lemmas.