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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., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Authors. Published by Elsevier B.V.)

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., Competing Interests: The authors have declared that no competing interests exists., (Copyright: © 2024 Shaikh et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Detecting forged handwriting is important in a wide variety of machine learning applications, and it is challenging when the input images are degraded with noise and blur. This article presents a new model based on conformable moments (CMs) and deep ensemble neural networks (DENNs) for forged handwriting detection in noisy and blurry environments. Since CMs involve fractional calculus with the ability to model nonlinearities and geometrical moments as well as preserving spatial relationships between pixels, fine details in images are preserved. This motivates us to introduce a DENN classifier, which integrates stenographic kernels and spatial features to classify input images as normal (original, clean images), altered (handwriting changed through copy-paste and insertion operations), noisy (added noise to original image), blurred (added blur to original image), altered-noise (noise is added to the altered image), and altered-blurred (blur is added to the altered image). To evaluate our model, we use a newly introduced dataset, which comprises handwritten words altered at the character level, as well as several standard datasets, namely ACPR 2019, ICPR 2018-FDC, and the IMEI dataset. The first two of these datasets include handwriting samples that are altered at the character and word levels, and the third dataset comprises forged International Mobile Equipment Identity (IMEI) numbers. Experimental results demonstrate that the proposed method outperforms the existing methods in terms of classification rate.

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., (© 2023. The Author(s).)

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., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Author(s).)

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., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Authors.)

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., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Authors. Published by Elsevier B.V.)

For heating, ventilation or air conditioning purposes in massive multistory building constructions, ducts are a common choice for air supply, return, or exhaust. Rapid population expansion, particularly in industrially concentrated areas, has given rise to a tradition of erecting high-rise buildings in which contaminated air is removed by making use of vertical ducts. For satisfying the enormous energy requirements of such structures, high voltage wires are used which are typically positioned near the ventilation ducts. This leads to a consequent motivation of studying the interaction of magnetic field (MF) around such wires with the flow in a duct, caused by vacuum pump or exhaust fan etc. Therefore, the objective of this work is to better understand how the established (thermally and hydrodynamically) movement in a perpendicular square duct interacts with the MF formed by neighboring current-carrying wires. A constant pressure gradient drives the flow under the condition of uniform heat flux across the unit axial length, with a fixed temperature on the duct periphery. After incorporating the flow assumptions and dimensionless variables, the governing equations are numerically solved by incorporating a finite volume approach. As an exclusive finding of the study, we have noted that MF caused by the wires tends to balance the flow reversal due to high Raleigh number. The MF, in this sense, acts as a balancing agent for the buoyancy effects, in the laminar flow regime., (© 2022. The Author(s).)

The flow of a fluid across a revolving disc has several technical and industrial uses. Examples of rotating disc flows include centrifugal pumps, viscometers, rotors, fans, turbines, and spinning discs. An important technology with implications for numerous treatments utilized in numerous sectors is the use of hybrid nanofluids (HNFs) to accelerate current advancements. Through investigation of ternary nanoparticle impacts on heat transfer (HT) and liquid movement, the thermal properties of tri-HNFs were to be ascertained in this study. Hall current, thermal radiation, and heat dissipation have all been studied in relation to the use of flow-describing equations. The ternary HNFs under research are composed of the nanomolecules aluminum oxide (Al 2 O 3 ), copper oxide (CuO), silver (Ag), and water (H 2 O). For a number of significant physical characteristics, the physical situation is represented utilizing the boundary layer investigation, which produces partial differential equations (PDEs). The rheology of the movement is extended and computed in a revolving setting under the assumption that the movement is caused by a rotatingfloppy. Before the solution was found using the finite difference method, complicated generated PDEs were transformed into corresponding ODEs (Keller Box method). A rise in the implicated influencing factors has numerous notable physical impacts that have been seen and recorded. The Keller Box method (KBM) approach is also delivered for simulating the determination of nonlinear system problems faced in developing liquid and supplementary algebraic dynamics domains. The rate of entropy formation rises as the magnetic field parameter and radiation parameter increase. Entropy production rate decreases as the Brinkman number and Hall current parameter become more enriched. The thermal efficiency of ternary HNFs compared to conventional HNFs losses to a low of 4.8% and peaks to 5.2%., (© 2022. The Author(s).)

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., (© 2022. The Author(s).)

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 (Al 2 O 3 ), copper oxide (CuO), silver (Ag), and water (H 2 O) 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., (© 2022. The Author(s).)

In order to understand the characteristics of bio-convection and moving microorganisms in flows of magnetized Walters-B nano-liquid, we developed a model employing Riga plate with stretchy sheet. The Buongiorno phenomenon is likewise employed to describe nano-liquid motion in the Walters-B fluid. Expending correspondence transformations, the partial differential equation (PDE) control system has been transformed into an ordinary differential equation (ODE) control system. The COMSOL program is used to generate mathematical answers for non-linear equations by employing the Galerkin finite element strategy (G-FEM). Utilizing logical and graphical metrics, temperature, velocity, and microbe analysis are all studied. Various estimates of well-known physical features are taken into account while calculating nanoparticle concentrations. It is demonstrated that this model's computations directly relate the temperature field to the current Biot number and parameter of the Walters-B fluid. The temperature field is increased to increase the approximations of the current Biot number and parameter of the Walters-B fluid., (© 2022. The Author(s).)

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., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2022 The Author(s).)

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., Competing Interests: The authors declare no competing financial interest., (© 2022 The Authors. Published by American Chemical Society.)

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., Competing Interests: Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://dx.doi.org/10.21037/qims-21-15). The authors have no conflicts of interest to declare., (2022 Quantitative Imaging in Medicine and Surgery. All rights reserved.)

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., Competing Interests: Competing interestsThe authors declare that they have no competing interests., (© The Author(s) 2022.)

A novel hybrid nanofluid was explored in order to find an efficient heat-transmitting fluid to replace standard fluids and revolutionary nanofluids. By using tangent hyperbolic hybrid combination nanoliquid with non-Newtonian ethylene glycol (EG) as a basis fluid and a copper (Cu) and titanium dioxide (TiO 2 ) mixture, this work aims to investigate the viscoelastic elements of the thermal transferring process. Flow and thermal facts, such as a slippery extended surface with magnetohydrodynamic (MHD), suction/injection, form factor, Joule heating, and thermal radiation effects, including changing thermal conductivity, were also integrated. The Keller-Box method was used to perform collective numerical computations of parametric analysis using governing equivalences. In the form of graphs and tables, the results of TiO 2 -Cu/EG hybrid nanofluid were compared to those of standard Cu/EG nanofluid in important critical physical circumstances. The entropy generation study was used to examine energy balance and usefulness for important physically impacting parameters. Detailed scrutiny on entropy development get assisted with Weissenberg number, magnetic parameter, fractional volumes, injection parameter, thermal radiation, variable thermal conductivity, Biot number, shape variation parameter, Reynolds and Brinkman number. Whereas the entropy gets resisted for slip and suction parameter. In this case, spotted entropy buildup with important parametric ranges could aid future optimization., (© 2021. The Author(s).)

Recently, various studied were presented to describe the population dynamic of covid-19. In this effort, we aim to introduce a different vitalization of the growth by using a controller term. Our method is based on the concept of conformable calculus, which involves this term. We investigate a system of coupled differential equations, which contains the dynamics of the diffusion among infected and asymptomatic characters. Strong control is considered due to the social separation. The result is consequently associated with a macroscopic law for the population. This dynamic system is useful to recognize the behavior of the growth rate of the infection and to confirm if its control is correctly functioning. A unique solution is studied under self-mapping properties. The periodicity of the solution is examined by using integral control and the optimal control is discussed in the sequel., Competing Interests: Competing interestsThe authors declare that they have no competing interests., (© The Author(s) 2021.)

There are different approaches that indicate the dynamic of the growth of microbe. In this research, we simulate the growth by utilizing the concept of fractional calculus. We investigate a fractional system of integro-differential equations, which covers the subtleties of the diffusion between infected and asymptomatic cases. The suggested system is applicable to distinguish the presentation of growth level of the infection and to approve if its mechanism is positively active. An optimal solution under simulation mapping assets is considered. The estimated numerical solution is indicated by employing the fractional Tutte polynomials. Our methodology is based on the Atangana-Baleanu calculus (ABC). We assess the recommended system by utilizing real data., Competing Interests: Competing interestsThe authors declare that they have no competing interests., (© The Author(s) 2021.)

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.

Introduction: The Internet of Things (IoT) comprises of various smart devices for the sharing of sensed data through online services. People will be directly contacted to check their health parameters and the reports will be collected centrally through smart devices. The requirement is protection of messages during the exchange of data between sender and receiver in order to tackle human malicious attacks. Various signature-based schemes are discussed in the literature to provide secure communication. Smart devices however require lightweight tasks by ensuring critical safety strengths. An important problem in the signature based method is that it incurs more computational expenses for signing and verification process in large numbers., Objectives: In this study, we introduced an efficient Short Signature Scheme (SSS) that uses Fractional Chaotic Map (FCM) for secure communication in IoT based smart devices, the security of which is closely related to a random oracle based on FCM assumption., Methods: In this study, we have designed new short signature scheme using FCM. The presented scheme consist of four sub-algorithm as follows: setup, key generation, signing and verification. We have used less rigorous operations based on the FCM to carry out signing and verification procedures, similar to human signing on valid documents and then verifying them as per witness., Results: The proposed SSS offers a better security assurance than currently established signature schemes. The key advantage of the SSS over the DSA schemes is that at the verification stage and signing period it takes less computation; it retains the degree of protection. The presented SSS takes less bandwidth for storage, communication, and computing resources; particularly applicable to wireless devices and smart cards., Conclusion: We concluded that the uses of fractional chaotic maps is more effective for secure communication in human-centered IoT to present a provably secure short signature technique., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2021 The Authors. Published by Elsevier B.V. on behalf of Cairo University.)

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.

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%.

Lately, many studies were offered to introduce the population dynamics of COVID-19. In this investigation, we extend different physical conditions of the growth by employing fractional calculus. We study a system of coupled differential equations, which describes the dynamics of the infection spreading between infected and asymptomatic styles. The healthy population properties are measured due to the social meeting. The result is associated with a macroscopic law for the population. This dynamic system is appropriate to describe the performance of growth rate of the infection and to verify if its control is appropriately employed. A unique solution, under self-mapping possessions, is investigated. Approximate solutions are presented by utilizing fractional integral of Chebyshev polynomials. Our methodology is based on the Atangana-Baleanu calculus, which provides various activity results in the simulation. We tested the suggested system by using live data. We found positive action in the graphs., Competing Interests: Competing interestsThe authors declare no conflict of interest., (© The Author(s) 2020.)

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., Competing Interests: The authors declare no conflict of interest.

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.

Background and Objectives: The MRI brain tumors segmentation is challenging due to variations in terms of size, shape, location and features' intensity of the tumor. Active contour has been applied in MRI scan image segmentation due to its ability to produce regions with boundaries. The main difficulty that encounters the active contour segmentation is the boundary tracking which is controlled by minimization of energy function for segmentation. Hence, this study proposes a novel fractional Wright function (FWF) as a minimization of energy technique to improve the performance of active contour without edge method., Method: In this study, we implement FWF as an energy minimization function to replace the standard gradient-descent method as minimization function in Chan-Vese segmentation technique. The proposed FWF is used to find the boundaries of an object by controlling the inside and outside values of the contour. In this study, the objective evaluation is used to distinguish the differences between the processed segmented images and ground truth using a set of statistical parameters; true positive, true negative, false positive, and false negative., Results: The FWF as a minimization of energy was successfully implemented on BRATS 2013 image dataset. The achieved overall average sensitivity score of the brain tumors segmentation was 94.8 ± 4.7%., Conclusions: The results demonstrate that the proposed FWF method minimized the energy function more than the gradient-decent method that was used in the original three-dimensional active contour without edge (3DACWE) method., (Copyright © 2018 Elsevier B.V. All rights reserved.)

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 biological dynamic system carries engineering properties such as control systems and signal processing (or image processing) addicted to molecular biology at the level of bio-molecular communication networks. Dynamical system features and signal reply functions of cellular signaling pathways are some of the main topics in biological dynamic systems (for example the biological segmentation). In the present paper, we introduce new generalized hybrid time-space dynamical systems of growing bacteria. We impose the approximate analytic solution for the system. The generalization adapted the concepts of the Riemann-Liouville fractional operators for time and the Srivastava-Owa fractional operators for space. Moreover, we introduce a numerical perturbation method of two operators to obtain the approximate solutions. We establish the existence and uniqueness results and impose some applications in the sequel. Moreover, we study the Ulam stability and apply these stable solutions to improve the segmentation of a class of growing bacteria., (Copyright © 2017 Elsevier Inc. All rights reserved.)

In this paper, we consider a low initial population model. Our aim is to study the periodicity computation of this model by using neutral differential equations, which are recognized in various studies including biology. We generalize the neutral Rayleigh equation for the third-order by exploiting the model of fractional calculus, in particular the Riemann-Liouville differential operator. We establish the existence and uniqueness of a periodic computational outcome. The technique depends on the continuation theorem of the coincidence degree theory. Besides, an example is presented to demonstrate the finding.

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.

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.

Recently, the study of the fractional formal (operators, polynomials and classes of special functions) has been increased. This study not only in mathematics but extended to another topics. In this effort, we investigate a generalized integro-differential operator [Formula: see text] defined by a fractional formal (fractional differential operator) and study some its geometric properties by employing it in new subclasses of analytic univalent functions.

Fractional differential equations have been discussed in this study. We utilize the Riemann-Liouville fractional calculus to implement it within the generalization of the well known class of differential equations. The Rayleigh differential equation has been generalized of fractional second order. The existence of periodic and positive outcome is established in a new method. The solution is described in a fractional periodic Sobolev space. Positivity of outcomes is considered under certain requirements. We develop and extend some recent works. An example is constructed.

Recently, the generalized hypergeometric function is extended by utilizing the Beta function. Based on this type of function, we introduce a new operator in the open unit disk. The present article investigates some subordination and superordination results for certain normalized analytic functions in the open unit disk, which are acted upon by the generalized Noor integral operator. Some of outcomes improve and generalize previously known outcomes.

Smoking problem is considered as one of the hot topics for many years. In spite of overpowering facts about the dangers, smoking is still a bad habit widely spread and socially accepted. Many people start smoking during their gymnasium period. The discovery of the dangers of smoking gave a warning sign of danger for individuals. There are different statistical methods used to analyze the dangers of smoking. In this study, we apply an algebraic statistical method to analyze and classify real data using Markov basis for the independent model on the contingency table. Results show that the Markov basis based classification is able to distinguish different date elements. Moreover, we check our proposed method via information theory by utilizing the Shannon formula to illustrate which one of these alternative tables is the best in term of independent.

A mutation is ultimately essential for adaptive evolution in all populations. It arises all the time, but is mostly fixed by enzymes. Further, most do consider that the evolution mechanism is by a natural assortment of variations in organisms in line for random variations in their DNA, and the suggestions for this are overwhelming. The altering of the construction of a gene, causing a different form that may be communicated to succeeding generations, produced by the modification of single base units in DNA, or the deletion, insertion, or rearrangement of larger units of chromosomes or genes. This altering is called a mutation. In this paper, a mathematical model is introduced to this reality. The model describes the time and space for the evolution. The tool is based on a complex domain for the space. We show that the evolution is distributed with the hypergeometric function. The Boundedness of the evolution is imposed by utilizing the Koebe function.