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Autism Spectrum Disorder (ASD) is a neurological illness that degrades communication and interaction among others. Autism can be detected at any stage. Early detection of ASD is important in preventing the communication, interaction and behavioral outcomes of individuals. Hence, this research introduced the Fractional Whale-driving Driving Training-based Based Optimization with Convolutional Neural Network-based Transfer learning (FWDTBO-CNN_TL) for identifying ASD. Here, the FWDTBO is modelled by the incorporation of Fractional calculus (FC), Whale optimization algorithm (WOA) and Driving Training-based Optimization (DTBO) that trains the hyperparameters of CNN-TL. Moreover, the Convolutional Neural Networks (CNN) utilize the hyperparameters from trained models, like Alex Net and Shuffle Net in such a way that the CNN-TL is designed. To improve the detection efficiency, the nub region was extracted and carried out with the functional connectivity-based Whale Driving Training Optimization (WDTBO) algorithm. Moreover, the TL is tuned by the FWDTBO algorithm. The result reveals that the ASD detection technique, FWDTBO-CNN-TL acquired 90.7 % accuracy, 95.4 % sensitivity, 93.7 % specificity and 93 % f-measure with the ABIDE-II dataset.

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Goal: The goal of this study is to investigate the application of fractional-order calculus in modeling arterial compliance in human vascular aging. Methods: A novel fractional-order modified arterial Windkessel model that incorporates a fractional-order capacitor (FOC) element is proposed to capture the complex and frequency-dependent properties of arterial compliance. The model's performance is evaluated by verifying it using data collected from three different human subjects, with a specific focus on aortic pressure and flow rates. Results: The results show that the FOC model accurately captures the dynamics of arterial compliance, providing a flexible means to estimate central blood pressure distribution and arterial stiffness. Conclusions: This study demonstrates the potential of fractional-order calculus in advancing the modeling and characterization of arterial compliance in human vascular aging. The proposed FOC model can improve our understanding of the physiological changes in arterial compliance associated with aging and help to identify potential interventions for age-related cardiovascular diseases.

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Dynamic analysis, electrical coupling and synchronization control of the conformable FitzHugh-Nagumo neuronal models have been presented in this work. Firstly, equations of the Adomian-Decomposition-Method and conformable neuron model have been introduced. The Adomian-Decomposition-Method has been employed for the numerical simulation analysis, since it converges fast and provides serial solutions. Fractional order and external current stimulus have been considered as bifurcation parameters and their effects on neuron model dynamics have been examined in detail. Then, the electrical coupling of the two conformable neuronal models without any controller has been revealed and the significance of the coupling strength parameter has been evaluated. To eliminate impact of the coupling strength parameter on synchronization status of neurons, Lyapunov control method has been employed for synchronization control. In the last step, the numerical simulation studies have been experimentally verified using the Texas Instrument Delfino digital signal processor board. Numerical simulation results together with experimental validation have showed that the types of dynamics of the related neuron model are not affected from the change of the fractional order of conformable derivative, but the frequency of the dynamic response of the neuronal model is changed from the alteration of the fractional order. The frequency of response of the neuron model increases with decreasing values of the fractional order. On the other hand, if there is no synchronization control method, the coupled neuron models exhibit response ranging from synchronous to asynchronous depending on the sign and value of the coupling parameter. Additionally, decreasing values of the fractional order may allow the coupled neurons to enter the synchronous state more quickly due to increasing frequency of response of the neuronal model. Finally, the coupled neuron models could exhibit synchronous behavior, that is determined by calculating the standard deviation results, regardless of the value of the coupling parameter by using the Lyapunov control method.

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BACKGROUND: This study explores the diagnostic value of combining fractional-order calculus (FROC) diffusion-weighted model with simultaneous multi-slice (SMS) acceleration technology in distinguishing benign and malignant breast lesions. METHODS: 178 lesions (73 benign, 105 malignant) underwent magnetic resonance imaging with diffusion-weighted imaging using multiple b-values (14 b-values, highest 3000 s/mm2). Independent samples t-test or Mann-Whitney U test compared image quality scores, FROC model parameters (D,, ), and ADC values between two groups. Multivariate logistic regression analysis identified independent variables and constructed nomograms. Model discrimination ability was assessed with receiver operating characteristic (ROC) curve and calibration chart. Spearman correlation analysis and Bland-Altman plot evaluated parameter correlation and consistency. RESULTS: Malignant lesions exhibited lower D, and ADC values than benign lesions (P < 0.05), with higher values (P < 0.05). In SSEPI-DWI and SMS-SSEPI-DWI sequences, the AUC and diagnostic accuracy of D value are maximal, with D value demonstrating the highest diagnostic sensitivity, while value exhibits the highest specificity. The D and combined model had the highest AUC and accuracy. D and ADC values showed high correlation between sequences, and moderate. Bland-Altman plot demonstrated unbiased parameter values. CONCLUSION: SMS-SSEPI-DWI FROC model provides good image quality and lesion characteristic values within an acceptable time. It shows consistent diagnostic performance compared to SSEPI-DWI, particularly in D and values, and significantly reduces scanning time.

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In designing control systems, it is known that fractional-order proportional integral derivative (FOPID) controllers often provide greater flexibility than conventional proportional integral derivative (PID) controllers. This higher level of flexibility has proven to be extremely valuable for various applications such as vibration suppression in structural engineering. In this paper, we study the optimization of FOPID controllers using twelve well-established algorithms to minimize structural responses under seismic excitations. The algorithms include crystal structure algorithm (CryStAl), stochastic paint optimizer, particle swarm optimization, krill herd, harmony search, ant colony optimization, genetic algorithm, grey wolf optimizer, Harris hawks optimization, sparrow search algorithm, hippopotamus optimization algorithm, and duck swarm algorithm. In addition to highlighting the benefits of fractional calculus in structural control, this study provides a detailed analysis of FOPID controllers as well as a brief description of the algorithms used to optimize them. To evaluate the efficiency of the proposed techniques, two building models with different numbers of stories are examined. FOPID controllers are designed based on oustaloup's approximation and the El Centro earthquake data. Using five well-known metrics, the performances of the developed methods are evaluated against five earthquake scenarios, including the recent earthquake in Turkey. A non-parametric (Friedman) test is also employed to compare the algorithms based on their corresponding vibration reduction. The findings of this analysis show that CryStAl consistently performs better than the other algorithms for both building models, thus resulting in superior vibration suppression.

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In recent years, there has been a growing interest in incorporating fractional calculus into stochastic delay systems due to its ability to model complex phenomena with uncertainties and memory effects. The fractional stochastic delay differential equations are conventional in modeling such complex dynamical systems around various applied fields. The present study addresses a novel spectral approach to demonstrate the stability behavior and numerical solution of the systems characterized by stochasticity along with fractional derivatives and time delay. By bridging the gap between fractional calculus, stochastic processes, and spectral analysis, this work contributes to the field of fractional dynamics and enriches the toolbox of analytical tools available for investigating the stability of systems with delays and uncertainties. To illustrate the practical implications and validate the theoretical findings of our approach, some numerical simulations are presented.

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Accurate development of satellite maneuvers necessitates a broad orbital dynamical system and efficient nonlinear control techniques. For achieving the intended formation, a framework of a discrete fractional difference satellite model is constructed by the use of commensurate and non-commensurate orders for the control and synchronization of fractional-order chaotic satellite system. The efficacy of the suggested framework is evaluated employing a numerical simulation of the concerning dynamic systems of motion while taking into account multiple considerations such as Lyapunov exponent research, phase images and bifurcation schematics. With the aid of discrete nabla operators, we monitor the qualitative behavioural patterns of satellite systems in order to provide justification for the structure's chaos. We acquire the fixed points of the proposed trajectory. At each fixed point, we calculate the eigenvalue of the satellite system's Jacobian matrix and check for zones of instability. The outcomes exhibit a wide range of multifaceted behaviours resulting from the interaction with various fractional-orders in the offered system. Additionally, the sample entropy evaluation is employed in the research to determine complexities and endorse the existence of chaos. To maintain stability and synchronize the system, nonlinear controllers are additionally provided. The study highlights the technique's vulnerability to fractional-order factors, resulting in exclusive, changing trends and equilibrium frameworks. Because of its diverse and convoluted behaviour, the satellite chaotic model is an intriguing and crucial subject for research.

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Evolution equations with convolution-type integral operators have a history of study, yet a gap exists in the literature regarding the link between certain convolution kernels and new models, including delayed and fractional differential equations. We demonstrate, starting from the logistic model structure, that classical, delayed, and fractional models are special cases of a framework using a gamma Mittag-Leffler memory kernel. We discuss and classify different types of this general kernel, analyze the asymptotic behavior of the general model, and provide numerical simulations. A detailed classification of the memory kernels is presented through parameter analysis. The fractional models we constructed possess distinctive features as they maintain dimensional balance and explicitly relate fractional orders to past data points. Additionally, we illustrate how our models can reproduce the dynamics of COVID-19 infections in Australia, Brazil, and Peru. Our research expands mathematical modeling by presenting a unified framework that facilitates the incorporation of historical data through the utilization of integro-differential equations, fractional or delayed differential equations, as well as classical systems of ordinary differential equations.

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Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a novel virus known as coronavirus 2 (SARS-CoV-2) that affects the pulmonary structure and results in the coronavirus illness 2019 (COVID-19). Tuberculosis (TB) and COVID-19 codynamics have been documented in numerous nations. Understanding the complexities of codynamics is now critically necessary as a consequence. The aim of this research is to construct a co-infection model of TB and COVID-19 in the context of fractional calculus operators, white noise and probability density functions, employing a rigorous biological investigation. By exhibiting that the system possesses non-negative and bounded global outcomes, it is shown that the approach is both mathematically and biologically practicable. The required conditions are derived, guaranteeing the eradication of the infection. Sensitivity analysis and bifurcation of the submodel are also investigated with system parameters. Furthermore, existence and uniqueness results are established, and the configuration is tested for the existence of an ergodic stationary distribution. For discovering the system's long-term behavior, a deterministic-probabilistic technique for modeling is designed and operated in MATLAB. By employing an extensive review, we hope that the previously mentioned approach improves and leads to mitigating the two diseases and their co-infections by examining a variety of behavioral trends, such as transitions to unpredictable procedures. In addition, the piecewise differential strategies are being outlined as having promising potential for scholars in a range of contexts because they empower them to include particular characteristics across multiple time frame phases. Such formulas can be strengthened via classical technique, power-law, exponential decay, generalized Mittag-Leffler kernels, probability density functions and random procedures. Furthermore, we get an accurate description of the probability density function encircling a quasi-equilibrium point if the effect of TB and COVID-19 minimizes the propagation of the codynamics. Consequently, scholars can obtain better outcomes when analyzing facts using random perturbations by implementing these strategies for challenging issues. Random perturbations in TB and COVID-19 co-infection are crucial in controlling the spread of an epidemic whenever the suggested circulation is steady and the amount of infection eliminated is closely correlated with the random perturbation level.

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A significant modification in photoinduced energy transfer in cancer cells is reported by the assistance of a dynamic modulation of the beam size of laser irradiation. Human lung epithelial cancer cells in monolayer form were studied. In contrast to the quantum and thermal ablation effect promoted by a standard focused Gaussian beam, a spatially modulated beam can caused around 15% of decrease in the ablation threshold and formation of a ring-shaped distribution of the photothermal transfer effect. Optical irradiation was conducted in A549 cells by a 532 nm single-beam emerging from a Nd:YVO4 system. Ablation effects derived from spatially modulated convergent waves were controlled by an electrically focus-tunable lens. The proposed chaotic behavior of the spatial modulation followed an Arneodo chaotic oscillator. Fractional dynamic thermal transport was analyzed in order to describe photoenergy in propagation through the samples. Immediate applications of chaos theory for developing phototechnology devices driving biological functions or phototherapy treatments can be considered.

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It is mentioned that understanding linear and non-linear thermo-elasticity systems is important for understanding temperature, elasticity, stresses, and thermal conductivity. One of the most crucial aspects of the current research is the solution to these systems. The fractional form of several thermo-elastic systems is explored, and elegant solutions are provided. The solutions of fractional and integer thermo-elastic systems are further discussed using tables and diagrams. The closed contact between the LRPSM and exact solutions is displayed in the graphs. Plotting fractional problem solutions demonstrates their convergence towards integer-order problem solutions for suitable modeling. The tables confirm that greater precision is rapidly attained as the terms of the derived series solution increase. The faster convergence and stability of the suggested method support its modification for other fractional non-linear complex systems in nature.

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This work reports the dielectric behavior of the biopolymer ethyl cellulose (EC) observed from transient currents experiments under the action of a direct current (DC) electric field (~107 V/m) under vacuum conditions. The viscoelastic response of the EC was evaluated using dynamic mechanical analysis (DMA), observing a mechanical relaxation related to glass transition of around ~402 K. Furthermore, we propose a mathematical framework that describes the transient current in EC using a fractional differential equation, whose solution involves the Mittag-Leffler function. The fractional order, between 0 and 1, is related to the energy dissipation rate and the molecular mobility of the polymer. Subsequently, the conduction mechanisms are considered, on the one hand, the phenomena that occur through the polymer-electrode interface and, on the other hand, those which manifest themselves in the bulk material. Finally, alternating current (AC) conductivity measurements above the glass transition temperature (~402 K) and in a frequency domain from 20 Hz to 2 MHz were carried out, observing electrical conduction described by the segmental movements of the polymeric chains. Its electrical properties also position EC as a potential candidate for electrical, electronics, and mechatronics applications.

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This paper aims to demonstrate a numerical strategy via finite difference formulations for time fractional reaction-diffusion models which are ubiquitous in chemical and biological phenomena. The time-fractional derivative is considered in the Caputo sense for both linear and nonlinear problems. First, the Caputo derivative is replaced with a quadrature formula, then an implicit method is used for the remaining part. In the linear case, the proposed strategy reduces the time fractional models into linear simultaneous equations. In nonlinear cases, Quasilinearization is utilized to tackle the nonlinear parts. With this strategy, solutions of the fractional system transform into linear algebraic systems which are easy to solve. Next, the Von Neumann method is implemented to examine the stability of the scheme which discloses that the scheme is unconditionally stable. Further, the applicability of the presented scheme is tested with different linear and nonlinear models which include the one dimensional Schnakenberg and Gray-Scott models, and one and two dimensional Brusselator models. To analyze the accuracy of the present technique two norms namely, L ∞ and L 2 , and relative error are addressed. Moreover, the obtained outcomes are shown tabulated and graphically which identifies that the scheme properly works for the time fractional reaction-diffusion systems.

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Recently, fuzzy dispersion entropy (DispEn) has attracted much attention as a new nonlinear dynamics method that combines the advantages of both DispEn and fuzzy entropy. However, it suffers from limitation of insensitivity to dynamic changes. To solve this limitation, we proposed fractional fuzzy dispersion entropy (FFDispEn) based on DispEn, a novel fuzzy membership function and fractional calculus. The fuzzy membership function was defined based on the Euclidean distance between the embedding vector and dispersion pattern. Simulated signals generated by the one-dimensional (1D) logistic map were used to test the sensitivity of the proposed method to dynamic changes. Moreover, 29 subjects were recruited for an upper limb muscle fatigue experiment, during which surface electromyography (sEMG) signals of the biceps brachii muscle were recorded. Both simulated signals and sEMG signals were processed using a sliding window approach. Sample entropy (SampEn), DispEn and FFDispEn were separately used to calculate the complexity of each frame. The sensitivity of different algorithms to the muscle fatigue process was analyzed using fitting parameters through linear fitting of the complexity of each frame signal. The results showed that for simulated signals, the larger the fractional order q, the higher the sensitivity to dynamic changes. Moreover, DispEn performed poorly in the sensitivity to dynamic changes compared with FFDispEn. As for muscle fatigue detection, the FFDispEn value showed a clear declining tendency with a mean slope of -1.658 × 10-3 as muscle fatigue progresses; additionally, it was more sensitive to muscle fatigue compared with SampEn (slope: -0.4156 × 10-3) and DispEn (slope: -0.1675 × 10-3). The highest accuracy of 97.5% was achieved with the FFDispEn and support vector machine (SVM). This study provided a new useful nonlinear dynamic indicator for sEMG signal processing and muscle fatigue analysis. The proposed method may be useful for physiological and biomedical signal analysis.

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The aim of this study is to develop and validate a unifying kinetic model for microvascular transport by introducing an impulse response function that incorporates essential physiological parameters and integrates key features of existing models. This new methodology combines a one-compartment model of fractional order with a model that uses the gamma distribution to describe the distribution of capillary transit times. Central to this model are two primary parameters: [Formula: see text], representing the kurtosis of residue times, and [Formula: see text], signifying the width of the distribution of capillary transit times within a tissue voxel. To validate this proposed model, data from dynamic contrast-enhanced magnetic resonance imaging (DCI-MRI) were employed and the findings were compared with three existing models. Using the Akaike information criterion for model selection, the results demonstrate that the integrative model, especially at elevated blood flow rates, frequently offers superior fits in comparison to constrained models.

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This study presents a fractional calculus model as a generalized kinetic model for estimating the maximum methane yield and degradation kinetics in biomethane potential (BMP) assays, a key analytical method in anaerobic digestion research and application. The fractional model outperformed common first-order kinetic models by yielding superior data fitting and properly managing substrate heterogeneity. The fractional model showed robust performance in mono-digestion, co-digestion and pre-treatment BMP assays with or without presence of large tailing or sigmoidal patterns in the BMP curve. The main advantage of the fractional model over other models is its ability to capture the complexities of the methane production process without losing model accuracy. Assessment of the mathematical model revealed that for fractional orders greater than 0.8 the Mittag-Leffler sequence could be transformed into a more computationally efficient exponential function.

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This paper proposes a fractional-order time-varying sliding mode control method with predefined-time convergence for a class of arbitrary-order nonlinear control systems with compound disturbances. The method has global robustness and strongly predefined-time stability. All state errors of the system can converge to zero at a desired time, which can be set arbitrarily with a simple parameter. The strongly predefined-time convergence of the system is clearly demonstrated by the analytic expression of state error, which is obtained by solving fractional-order differential equations corresponding to the sliding mode function. The simulation results show that the proposed method still has good control performance in the presence of input saturation and external interference.

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The mathematical oncology has received a lot of interest in recent years since it helps illuminate pathways and provides valuable quantitative predictions, which will shape more effective and focused future therapies. We discuss a new fractal-fractional-order model of the interaction among tumor cells, healthy host cells and immune cells. The subject of this work appears to show the relevance and ramifications of the fractal-fractional order cancer mathematical model. We use fractal-fractional derivatives in the Caputo senses to increase the accuracy of the cancer and give a mathematical analysis of the proposed model. First, we obtain a general requirement for the existence and uniqueness of exact solutions via Perov's fixed point theorem. The numerical approaches used in this paper are based on the Grünwald-Letnikov nonstandard finite difference method due to its usefulness to discretize the derivative of the fractal-fractional order. Then, two types of stabilities, Lyapunov's and Ulam-Hyers' stabilities, are established for the Incommensurate fractional-order and the Incommensurate fractal-fractional, respectively. The numerical results of this study are compatible with the theoretical analysis. Our approaches generalize some published ones because we employ the fractal-fractional derivative in the Caputo sense, which is more suitable for considering biological phenomena due to the significant memory impact of these processes. Aside from that, our findings are new in that we use Perov's fixed point result to demonstrate the existence and uniqueness of the solutions. The way of expressing the Ulam-Hyers' stabilities by utilizing the matrices that converge to zero is also novel in this area.

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Dielectric and thermal properties of polyvinyl butyral (PVB) were studied in this work, using dynamic electrical analysis (DEA) at frequencies from 100 Hz to 1 MHz and temperatures from 293 K to 473 K. Two electrical relaxation processes were investigated: glass transition and interfacial polarization. Above the glass transition temperature (~343 K), interfacial polarization dominates conductive behavior in polyvinyl butyral. The framework of the complex electric modulus was used to obtain information about interfacial polarization. The viscoelastic behavior was analyzed through dynamic mechanical analysis (DMA), where only the mechanical manifestation of the glass transition is observed. The experimental results from dielectric measurements were analyzed with fractional calculus, using a fractional Debye model with one cap-resistor. We were successful in applying the complex electric modulus because we had a good correlation between data and theoretical predictions. The fractional order derivative is an indicator of the energy dissipated in terms of molecular mobility, and the calculated values close to 1 suggest a conductive behavior at temperatures above the glass transition temperature of PVB.

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We address mathematical modelling of respiratory mechanics and put forward a model based on double-exponential and fractional calculus for parameter estimation, model simulation, and evaluation based on actual data. Our model has been implemented on a publicly available executable code with adjustable parameters, making it suitable for different applications. Our analysis represents the first application of fractional calculus and double-exponential modelling to respiratory mechanics, and allows us to propose a hybrid model fitting experimental data in different ventilation modes. Furthermore, our model can be used to study the mechanical features of the respiratory system, improve the safety of ventilation techniques, reduce ventilation damages, and provide strong support for fast and adaptive determination of ventilation parameters.