Susceptible-Infected-Susceptible Epidemic Discrete Dynamic System Based on Tsallis Entropy.

This investigation deals with a discrete dynamic system of susceptible-infected-susceptible epidemic (SISE) using the Tsallis entropy. We investigate the positive and maximal solutions of the system. Stability and equilibrium are studied. Moreover, based on the Tsallis entropy, we shall formulate a new design for the basic reproductive ratio. Finally, we apply the results on live data regarding COVID-19.

Classification of Covid-19 Coronavirus, Pneumonia and Healthy Lungs in CT Scans Using Q-Deformed Entropy and Deep Learning Features.

Many health systems over the world have collapsed due to limited capacity and a dramatic increase of suspected COVID-19 cases. What has emerged is the need for finding an efficient, quick and accurate method to mitigate the overloading of radiologists' efforts to diagnose the suspected cases. This study presents the combination of deep learning of extracted features with the Q-deformed entropy handcrafted features for discriminating between COVID-19 coronavirus, pneumonia and healthy computed tomography (CT) lung scans. In this study, pre-processing is used to reduce the effect of intensity variations between CT slices. Then histogram thresholding is used to isolate the background of the CT lung scan. Each CT lung scan undergoes a feature extraction which involves deep learning and a Q-deformed entropy algorithm. The obtained features are classified using a long short-term memory (LSTM) neural network classifier. Subsequently, combining all extracted features significantly improves the performance of the LSTM network to precisely discriminate between COVID-19, pneumonia and healthy cases. The maximum achieved accuracy for classifying the collected dataset comprising 321 patients is 99.68%.

MRI Brain Classification Using the Quantum Entropy LBP and Deep-Learning-Based Features.

Brain tumor detection at early stages can increase the chances of the patient's recovery after treatment. In the last decade, we have noticed a substantial development in the medical imaging technologies, and they are now becoming an integral part in the diagnosis and treatment processes. In this study, we generalize the concept of entropy difference defined in terms of Marsaglia formula (usually used to describe two different figures, statues, etc.) by using the quantum calculus. Then we employ the result to extend the local binary patterns (LBP) to get the quantum entropy LBP (QELBP). The proposed study consists of two approaches of features extractions of MRI brain scans, namely, the QELBP and the deep learning DL features. The classification of MRI brain scan is improved by exploiting the excellent performance of the QELBP-DL feature extraction of the brain in MRI brain scans. The combining all of the extracted features increase the classification accuracy of long short-term memory network when using it as the brain tumor classifier. The maximum accuracy achieved for classifying a dataset comprising 154 MRI brain scan is 98.80%. The experimental results demonstrate that combining the extracted features improves the performance of MRI brain tumor classification.

New Texture Descriptor Based on Modified Fractional Entropy for Digital Image Splicing Forgery Detection.

Forgery in digital images is immensely affected by the improvement of image manipulation tools. Image forgery can be classified as image splicing or copy-move on the basis of the image manipulation type. Image splicing involves creating a new tampered image by merging the components of one or more images. Moreover, image splicing disrupts the content and causes abnormality in the features of a tampered image. Most of the proposed algorithms are incapable of accurately classifying high-dimension feature vectors. Thus, the current study focuses on improving the accuracy of image splicing detection with low-dimension feature vectors. This study also proposes an approximated Machado fractional entropy (AMFE) of the discrete wavelet transform (DWT) to effectively capture splicing artifacts inside an image. AMFE is used as a new fractional texture descriptor, while DWT is applied to decompose the input image into a number of sub-images with different frequency bands. The standard image dataset CASIA v2 was used to evaluate the proposed approach. Superior detection accuracy and positive and false positive rates were achieved compared with other state-of-the-art approaches with a low-dimension of feature vectors.

Analytic Study of Complex Fractional Tsallis' Entropy with Applications in CNNs.

In this paper, we study Tsallis' fractional entropy (TFE) in a complex domain by applying the definition of the complex probability functions. We study the upper and lower bounds of TFE based on some special functions. Moreover, applications in complex neural networks (CNNs) are illustrated to recognize the accuracy of CNNs.

A New Local Fractional Entropy-Based Model for Kidney MRI Image Enhancement.

Kidney image enhancement is challenging due to the unpredictable quality of MRI images, as well as the nature of kidney diseases. The focus of this work is on kidney images enhancement by proposing a new Local Fractional Entropy (LFE)-based model. The proposed model estimates the probability of pixels that represent edges based on the entropy of the neighboring pixels, which results in local fractional entropy. When there is a small change in the intensity values (indicating the presence of edge in the image), the local fractional entropy gives fine image details. Similarly, when no change in intensity values is present (indicating smooth texture), the LFE does not provide fine details, based on the fact that there is no edge information. Tests were conducted on a large dataset of different, poor-quality kidney images to show that the proposed model is useful and effective. A comparative study with the classical methods, coupled with the latest enhancement methods, shows that the proposed model outperforms the existing methods.

A new mathematical model of the dynamic of psychotherapy.

The aim of the present study is to construct a mathematical model skilled in creating hard estimates about the dynamic of psychotherapy with a purpose of using it for better sequence therapists. The outcome of the calculations envisages a new viewpoint on the therapeutic relationship and a number of suitable visions. The proposed model is based on a class of fractional differential equations. This type of class was a generalized neutral differential equation of first order. Certain sufficient conditions for the existence of periodic outcomes have been imposed.

Generalized population dynamic operator with delay based on fractional calculus.

In population dynamics, a growing population consumes more food than a matured one that depends upon condition of individual species. This hints to neutral equations. In the present study, certain sufficient conditions for the existence of periodic solutions to a generalized Rayleigh-type equation with state dependent delay, based on fractional calculus concept was investigated.

Classification of tomato leaf images for detection of plant disease using conformable polynomials image features.

Plant diseases can spread rapidly, leading to significant crop losses if not detected early. By accurately identifying diseased plants, farmers can target treatment only to the affected areas, reducing the number of pesticides or fungicides needed and minimizing environmental impact. Tomatoes are among the most significant and extensively consumed crops worldwide. The main factor affecting crop yield quantity and quality is leaf disease. Various diseases can affect tomato production, impacting both yield and quality. Automated classification of leaf images allows for the early identification of diseased plants, enabling prompt intervention and control measures. Many creative approaches to diagnosing and categorizing specific illnesses have been widely employed. The manual method is costly and labor-intensive. Without the assistance of an agricultural specialist, disease detection can be facilitated by image processing combined with machine learning algorithms. In this study, the diseases in tomato leaves will be detected using new feature extraction method using conformable polynomials image features for accurate solution and faster detection of plant diseases through a machine learning model. The methodology of this study based on:•Preprocessing, feature extraction, dimension reduction and classification modules.•Conformable polynomials method is used to extract the texture features which is passed classifier.•The proposed texture feature is constructed by two parts the enhanced based term, and the texture detail part for textual analysis.•The tomato leaf samples from the plant village image dataset were used to gather the data for this model. The disease detected are 98.80 % accurate for tomato leaf images using SVM classifier. In addition to lowering financial loss, the suggested feature extraction method can help manage plant diseases effectively, improving crop yield and food security.

Mathematical modeling and performance evaluation of Ducted Horizontal-axis Helical Wind Turbines: Insights into aerodynamics and efficiency.

With the escalating demand for energy, there is a growing focus on decentralized, small-scale energy infrastructure. The success of new turbines in this context is notable. However, many of these turbines do not follow many of the basic ideas established to evaluate their performance, leaving no precise technique or mathematical model. This research developed a Ducted Horizontal-axis Helical Wind Turbine (DHAHWT). The DHAHWT is a duct-mounted helical savonius turbine with a venturi and diffuser to improve flow. Unlike a vertical axis helical savonius turbine, DHAHWT revolves roughly parallel to the wind, making it a horizontal turbine. This complicates mathematical and theoretical analysis. This study created a DHAHWT mathematical model. COMSOL simulations utilizing Menter's Shear Stress Transport model (SST) across an incoming velocity range of 1m/s to 4m/s were used to evaluate the turbine's interaction with the wind. MATLAB was used to train an artificial neural network (ANN) utilizing COMSOL data to obtain greater velocity data. The Mean Average Percentage Error (MAPE) and Root Mean Square Error (RMSE) of ANN data were found to be 3%, indicating high accuracy. Further, using advanced statistical methods the Pearson's correlation coefficient was calculated resulting in a better understanding of the relationship of between incoming velocity and velocity at different sections of the wind turbine. This study will shed light on the aerodynamics and working of DHAHWT.

Studies on a new K-symbol analytic functions generated by a modified K-symbol Riemann-Liouville fractional calculus.

Analytic functions are very helpful in many mathematical and scientific uses, such as complex integration, potential theory, and fluid dynamics, due to their geometric features. Particularly conformal mappings are widely used in physics and engineering because they make it possible to convert complex physical issues into simpler ones with simpler answers. We investigate a novel family of analytic functions in the open unit disk using the K-symbol fractional differential operator type Riemann-Liouville fractional calculus of a complex variable. For the analysis and solution of differential equations containing many fractional orders, it offers a potent mathematical framework. There are ongoing determinations to strengthen the mathematical underpinnings of K-symbol fractional calculus theory and investigate its applications in various fields.•Normalization is presented for the K-symbol fractional differential operator. Geometric properties are offered of the proposed K-symbol fractional differential operator, such as the starlikeness property and hence univalency in the open unit disk.•The formula of the Alexander integral involving the proposed operator is suggested and studied its geometric properties such as convexity.•Examples are illustrated to fit our pure result. Here, the technique is based on the concepts of geometric function theory in the open unit disk, such as the subordination and Jack lemma.

A new X-ray images enhancement method using a class of fractional differential equation.

Many image-processing applications heavily depend on the quality of medical images. Due to the unpredictable variation in the captured images, medical images frequently have problems with noise or low contrast; therefore, improving medical imaging is a challenging task. For better treatment, physicians need images with good contrast to provide the most detailed picture of the disease. The generalized k-differential equation based on the k-Caputo fractional differential operator (K-CFDO) is used in this study to determine the energy of the image pixels to improve the visual quality and provide a clearly defined problem. The logic behind using the K-CFDO approach in image enhancement is the ability of K-CFDO to efficiently capture high-frequency details using the probability of pixels as well as preserve the fine image details. Moreover, the visual quality of X-ray images is improved by performing a low-contrast X-ray image enhancement.•Determine the energy of the image pixels for better pixel intensity enhancement.•Capture high frequency image details using the image probability of pixels. The findings of this study indicate that the average Brisque, Niqe, and Piqe values for the provided chest X-ray were found to be (Brisque=23.25, Niqe=2.8, Piqe21.58), and for the dental X-ray, they were (Brisque=21.12, Niqe=3.77, Piqe=23.49). The results of this study show potential improvements with the proposed enhancement methods that may contribute to increasing efficiency in healthcare processes at rural clinics. Generally, this model improves the details of medical images, which may aid medical staff throughout the diagnostic process by increasing the efficiency and accuracy of clinical decisions. Due to the improper setting of the suggested enhancing parameters, the current study included a limitation on image over-enhancement.

Multi-class deep learning architecture for classifying lung diseases from chest X-Ray and CT images.

Medical imaging is considered a suitable alternative testing method for the detection of lung diseases. Many researchers have been working to develop various detection methods that have aided in the prevention of lung diseases. To better understand the condition of the lung disease infection, chest X-Ray and CT scans are utilized to check the disease's spread throughout the lungs. This study proposes an automated system for the detection multi lung diseases in X-Ray and CT scans. A customized convolutional neural network (CNN) and two pre-trained deep learning models with a new image enhancement model are proposed for image classification. The proposed lung disease detection comprises two main steps: pre-processing, and deep learning classification. The new image enhancement algorithm is developed in the pre-processing step using k-symbol Lerch transcendent functions model which enhancement images based on image pixel probability. While, in the classification step, the customized CNN architecture and two pre-trained CNN models Alex Net, and VGG16Net are developed. The proposed approach was tested on publicly available image datasets (CT, and X-Ray image dataset), and the results showed classification accuracy, sensitivity, and specificity of 98.60%, 98.40%, and 98.50% for the X-Ray image dataset, respectively, and 98.80%, 98.50%, 98.40% for the CT scans dataset, respectively. Overall, the obtained results highlight the advantages of the image enhancement model as a first step in processing.

Irreversibility analysis of hydromagnetic nanofluid flow past a horizontal surface via Koo-Kleinstreuer-Li (KKL) model.

The goal of this research is to investigate the effects of Ohmic heating, heat generation, and viscous dissipative flow on magneto (MHD) boundary-layer heat transmission flowing of Jeffrey nanofluid across a stretchable surface using the Koo-Kleinstreuer-Li (KKL) model. Engine oil serves as the primary fluid and is suspended with copper oxide nanomolecules. The governing equations that regulate the flowing and heat transmission fields are partial-differential equations (PDEs) that are then converted to a model of non-linear ordinary differential equations (ODEs) via similarity transformation. The resultant ODEs are numerically resolved using a Keller box technique via MATLAB software that is suggested. Diagrams and tables are used to express the effects of various normal liquids, nanomolecule sizes, magneto parameters, Prandtl, Deborah, and Eckert numbers on the velocity field and temperature field. The outcomes display that the copper oxide-engine oil nanofluid has a lower velocity, drag force, and Nusselt number than the plain liquid, although the introduction of nanoparticles raises the heat. The heat transference rate is reduced by Eckert number, size of nanomolecules, and magneto parameter rising. Whilst, Deborah number is shown to enhance both the drag-force factor and the heat transfer rate. Furthermore, the discoveries reported are advantageous to upgrading incandescent lighting bulbs, heating, and cooling equipment, filament-generating light, energy generation, multiple heating devices, and other similar devices.

A new mathematical model of multi-faced COVID-19 formulated by fractional derivative chains.

It has been reported that there are seven different types of coronaviruses realized by individuals, containing those responsible for the SARS, MERS, and COVID-19 epidemics. Nowadays, numerous designs of COVID-19 are investigated using different operators of fractional calculus. Most of these mathematical models describe only one type of COVID-19 (infected and asymptomatic). In this study, we aim to present an altered growth of two or more types of COVID-19. Our technique is based on the ABC-fractional derivative operator. We investigate a system of coupled differential equations, which contains the dynamics of the diffusion between infected and asymptomatic people. The consequence is accordingly connected with a macroscopic rule for the individuals. In this analysis, we utilize the concept of a fractional chain. This type of chain is a fractional differential-difference equation combining continuous and discrete variables. The existence of solutions is recognized by formulating a matrix theory. The solution of the approximated system is shown to have a minimax point at the origin.

Mathematical model based on fractional trace operator for COVID-19 image enhancement.

The medical image enhancement is major class in the image processing which aims for improving the medical diagnosis results. The improving of the quality of the captured medical images is considered as a challenging task in medical image. In this study, a trace operator in fractional calculus linked with the derivative of fractional Rényi entropy is proposed to enhance the low contrast COVID-19 images. The pixel probability values of the input image are obtained first in the proposed image enhancement model. Then the covariance matrix between the input image and the probability of a pixel intensity of the input image to be calculated. Finally, the image enhancement is performed by using the convolution of covariance matrix result with the input image. The proposed enhanced image algorithm is tested against three medical image datasets with different qualities. The experimental results show that the proposed medical image enhancement algorithm achieves the good image quality assessments using both the BRISQUE, and PIQE quality measures. Moreover, the experimental results indicated that the final enhancement of medical images using the proposed algorithm has outperformed other methods. Overall, the proposed algorithm has significantly improved the image which can be useful for medical diagnosis process.

Second-order convergence analysis for Hall effect and electromagnetic force on ternary nanofluid flowing via rotating disk.

The purpose of this research was to estimate the thermal characteristics of tri-HNFs by investigating the impacts of ternary nanoparticles on heat transfer (HT) and fluid flow. The employment of flow-describing equations in the presence of thermal radiation, heat dissipation, and Hall current has been examined. Aluminum oxide (Al2O3), copper oxide (CuO), silver (Ag), and water (H2O) nanomolecules make up the ternary HNFs under study. The physical situation was modelled using boundary layer analysis, which generates partial differential equations for a variety of essential physical factors (PDEs). Assuming that a spinning disk is what causes the flow; the rheology of the flow is enlarged and calculated in a rotating frame. Before determining the solution, the produced PDEs were transformed into matching ODEs using the second order convergent technique (SOCT) also known as Keller Box method. Due to an increase in the implicated influencing elements, several significant physical effects have been observed and documented. For resembling the resolution of nonlinear system issues come across in rolling fluid and other computational physics fields.

A medical image enhancement based on generalized class of fractional partial differential equations.

BACKGROUND: The interest in using fractional calculus operators has grown in the field of image processing. Image enhancement is one of image processing tools that aims to improve the details of an image. The enhancement of medical images is a challenging task due to the unforeseeable variation in the quality of the captured images. METHODS: In this study, we present a mathematical model based on the class of fractional partial differential equations (FPDEs). The class is formulated by the proportional-Caputo hybrid operator (PCHO). Moreover, some properties of the geometric functions in the unit disk are applied to determine the upper bound solutions for this class of FPDEs. The upper bound solution is indicated in the relations of the general hypergeometric functions. The main advantage of FPDE lies in its capability to enhance the low contrast intensities through the proposed fractional enhanced operator. RESULTS: The proposed image enhancement algorithm is tested against brain and lungs computed tomography (CT) scans datasets of different qualities to show that it is robust and can withstand dramatic variations in quality. The quantitative results of Brisque, Piqe, SSEQ, and SAMGVG were 40.93%, 41.13%, 66.09%, and 31.04%, respectively for brain magnetic resonance imaging (MRI) images and 39.07, 41.33, 30.97, and 159.24 respectively for the CT lungs images. The comparative results show that the proposed image enhancement model achieves the best image quality assessments. CONCLUSIONS: Overall, this model significantly improves the details of the given datasets, and could potentially help the medical staff during the diagnosis process.

Effectiveness of Nonuniform Heat Generation (Sink) and Thermal Characterization of a Carreau Fluid Flowing across a Nonlinear Elongating Cylinder: A Numerical Study.

During thermal radiation treatments, heat therapies, and examination procedures like scans and X-rays, the cylindrical blood vessels may get stretched; meanwhile, the blood flow through those blood vessels may get affected due to temperature variations around them. To overcome this issue, this work was framed to explore the impact of heat transmission in a Carreau fluid flow (CFF) through a stretching cylinder in terms of the nonlinear stretching rate and irregular heat source/sink. Temperature-dependent thermal conductivity and thermal radiation are taken into consideration in this study. To tranform complicated partial differential equations into ordinary differential equations, appropriate similarity variables are used. For a limited set of instances, the derived series solutions are compared to previously published results. For linear and nonlinear stretching rates, graphs and tables are used to examine the influence of an irregular heat source/sink on fluid movement and heat transfer. The research outcomes demonstrate that the heat source and nonlinear stretching rate cause a disruption in the temperature distribution in the fluid region, which can alter the blood flow through the vessels. In all conditions except for the heat in an internal heat sink, the nonlinear stretching situation improves the velocity and heat profile. Furthermore, with the increase in the values of the Weissenberg number, the temperature profile shows opposing features in a shear-thickening fluid and shear-thinning fluid. For the former n > 1, the blood fluidity gets affected, restricting the free movement of blood. For the latter, n < 1, the phenomenon is reversed. Other industrial applications of this work are wire coating, plastic coverings, paper fabrication, fiber whirling, etc. In all of those processes, the fluid flow is manipulated by thermal conditions.

New optimum solutions of nonlinear fractional acoustic wave equations via optimal homotopy asymptotic method-2 (OHAM-2).

The second iteration of the optimal homotopy asymptotic technique (OHAM-2) has been protracted to fractional order partial differential equations in this work for the first time (FPDEs). Without any transformation, the suggested approach can be used to solve fractional-order nonlinear Zakharov-Kuznetsov equations. The Caputo notion of the fractional-order derivative, whose values fall within the closed interval [0, 1], has been taken into consideration. The method's appeal is that it provides an approximate solution after just one iteration. The suggested method's numerical findings have been contrasted with those of the variational iteration method, residual power series method, and perturbation iteration method. Through tables and graphs, the proposed method's effectiveness and dependability are demonstrated.