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The work reported in this paper deals with the study of a coupled system for fractional terminal value problems involving ψ-Hilfer fractional derivative. The existence and uniqueness theorems to the problem at hand are investigated. Besides, the stability analysis in the Ulam–Hyers sense of a given system is studied. Our discussion is based upon known fixed point theorems of Banach and Krasnoselskii. Examples are also provided to demonstrate the applicability of our results. [ABSTRACT FROM AUTHOR]

To have a more realistic model, in this paper, This manuscript is devoted to investigating a fractional-order mathematical model of Kouidere et al. That describes the dynamics of spread of African swine fever virus (ASFV). The aim of this work is to protect susceptible pigs from the virus, In our model, by including three controls which represent: the iron fencing and spraying pesticides and get rid. The aims of this paper is to reduce the number of infected pigs and ticks by using optimal control strategy and fractinal order derivation. Pontryagin's maximal principle is used to describe optimal controls with Caputo time-fractional derivative and the optimal system is resolved in an iterative manner. Numerical simulations are presented based on the presented method. We finished tis article with a conclusion. [ABSTRACT FROM AUTHOR]

In many industrial applications, reactive filters, which remove toxic substances using chemical reactions, prove very efficient and versatile. One such example is the removal of sulphur dioxide from flue gas by converting it into liquid sulphuric acid. In this paper, we extend a model developed in Kiradjiev et al. (SIAM J Appl Math 82:591–619, 2021) for the operation of a reactive filter to consider the long-time behaviour and determine how the filter becomes clogged with liquid and becomes inefficient. We explore how the parameters that govern the operation of the filter affect its efficiency and discuss optimal filtration strategies. We also consider a distinguished asymptotic limit in terms of the key dimensionless parameters and obtain an explicit solution that compares well with the numerical solution to the full problem. Finally, we compare the results of our model with those from a simplified model for a reactive filter considered in Breward and Kiradjiev (J Eng Math, 129(14):1–28, 2021). [ABSTRACT FROM AUTHOR]

In this paper, we deal with Caputo-type fractional differential inequality where there is a low-order fractional derivative with the term polynomial source. We investigate the nonexistence of nontrivial global solutions in a suitable space via the test function technique and some properties of fractional integrals. Finally, we demonstrate three examples to illustrate our results. The presented results are more general than those in the literature, which can be obtained as particular cases. [ABSTRACT FROM AUTHOR]

Fall armyworm (Spodoptera frugiperda), a highly destructive and fast spreading agricultural pest native to North and South America, poses a real threat to global food security. In this paper, to explore the dynamics and implications of fall armyworm outbreak in a field of maize biomass, we propose a new dynamical system for maize biomass and fall armyworm interaction via Caputo fractional-order operator, which is not only a nonlocal operator but also contains all characteristics concerned with memory of the dynamical system. We define the basic reproduction number, which represents the average number of newborns produced by one individual female moth during its life span. We establish that the basic reproduction number is a threshold quantity, which determines persistence and extinction of the pest. Finally, we simulate the Caputo system using the Adam–Bashforth–Moulton method to illustrate the main results. [ABSTRACT FROM AUTHOR]

This paper presents a state-of-art survey of the research on fractional-order (FO) modeling with parameter identification, and FO estimation methods for state of charge (SOC), state of health (SOH), and remaining usage life (RUL) of lithium-ion batteries (LIBs) mainly in recent five years. FO electrochemical models and six different types of FO equivalent circuit models (ECMs) are introduced in detail. Then, the corresponding tuning algorithm for parameters of these FO models are also provided in brief. Moreover, FO estimation methods for SOC are listed and analyzed, mainly including FO observers, and FO Kalman filters (FO-KFs). SOH and RUL estimation is another vital aspect for LIBs ageing and degradation monitoring, thus FO estimation methods proposed in recent research within five years are all listed. Finally, some suggestions that may be helpful for further research are proposed in conclusion. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of periodic solution of a delayed predator-prey model with M -predators and N -preys over the time scales. We derive sufficient conditions for the existence of a periodic solution with the help of continuation theorem of coincidence degree theory. At the end, we give an example with numerical simulations to illustrate our analytical findings. [ABSTRACT FROM AUTHOR]

The paper deals with monocular image-based sense and avoid assuming constant aircraft velocities and straight flight paths. From very limited two dimensional image information it finally characterizes the whole three dimensional collision situation by estimating the time to closest point of approach, the horizontal relative distance and its direction and the vertical relative distance also. The distances are relative to the intruder aircraft horizontal and vertical sizes. The overall estimated relative distance is the closest between the two aircraft in three dimension. So finally, every important information can be extracted to be used in a collision decision. The applicability of the developed method is presented in software-in-the-loop simulation test runs. Several intruder size and speed values are considered together with trajectories covering the whole three dimensional space. The horizontal intruder flight directions relative to the own aircraft cover 360∘ and the intruder can come from below ar above also. Detailed evaluation and discussion of the results is also included. Finally, the missed detection rate results to be superior (below 3% in every test scenario) though the false alarm rate results a bit high between 7-14%. [ABSTRACT FROM AUTHOR]

An important research area in life sciences is devoted to modeling, prediction, and dynamics of gene-expression patterns. As clearly understood in these days, this enterprise cannot become satisfactory without acknowledging the role of the environment. To a representation of past, present, and most likely future states, we also encounter measurement errors and uncertainties. This paper surveys and improves recent advances in understanding the foundations and interdisciplinary implications of the newly introduced gene–environment networks, and it integrates the important theme of carbon dioxide emission reduction into the networks and dynamics. We also introduce some operational and managerial issues of practical working and decision making, expressed in terms of sliding windows, quadrants ( modules) of parametric effects, and navigating ( controlling) between such effects and directing them. Given data from DNA microarray experiments and environmental records, we extract nonlinear ordinary differential equations that contain parameters that have to be determined. For this, we employ modern (Chebychevian) approximation and (generalized semi-infinite) optimization. After this is provided, time- discretized dynamical systems are studied. A combinatorial algorithm with polyhedra sequences allows to detect the region of parametric stability. Finally, we analyze the topological landscape of gene–environment networks with its structural (in)stability. By embedding as a module and investigating CO2 emission control and figuring out game theoretical aspects, we conclude. This pioneering work is theoretically elaborated, practically devoted to health care, medicine, education, living conditions, and environmental protection, and it invites the readers to future research. [ABSTRACT FROM AUTHOR]

Depending on a field study for one of the largest iron and paints warehouses in Egypt, this paper presents a new multi-item periodic review inventory model considering the refunding quantity cost. Through this field study, we found that the inventory level is monitored periodically at equal time intervals. Returning a part of the goods that were previously ordered is permitted. Also, a shortage is permissible to occur despite having orders, and it is a combination of the backorder and lost sales. This model has been applied in both crisp and fuzzy environments since the fuzzy case is more suitable for real-life than crisp. The Lagrange multiplier technique is used for solving the restricted mathematical model. Here, the demand is a random variable that follows the normal distribution with zero lead-time. Finally, the model is followed by a real application to clarify the model and prove its efficiency. [ABSTRACT FROM AUTHOR]

Effective tuberculosis (TB) control depends on case findings to discover infectious cases, investigation of contacts of those with TB, as well as appropriate treatment. Adherence and successful completion of the treatment are equally important. Unfortunately, due to a number of personal, psychosocial, economic, medical, and health service factors, a significant number of TB patients become irregular and default from treatment. In this paper, a mathematical model is developed to assess the impact of early therapy for latent TB and non-adherence on controlling TB transmission dynamics. Equilibrium states of the model are determined and their local stability is examined. With the aid of the center manifold theory, it is established that the model undergoes a backward bifurcation. Qualitative mathematical analysis of the model suggests that a high level of latent tuberculosis case findings, coupled with a decrease of defaulting rate, may be effective in controlling TB transmission dynamics in the community. Population-level effects of organized campaigns to improve early therapy and to guarantee successful completion of each treatment are evaluated through numerical simulations and presented in support of the analytical results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to analyze the recruitment effects of susceptible and infected individuals in order to assess the productivity of an organizational labor force in the presence of HIV/AIDS with preventive and HAART treatment measures in enhancing the workforce output. We consider constant controls as well as time-dependent controls. In the constant control case, we calculate the basic reproduction number and investigate the existence and stability of equilibria. The model is found to exhibit backward and Hopf bifurcations, implying that for the disease to be eradicated, the basic reproductive number must be below a critical value of less than one. We also investigate, by calculating sensitivity indices, the sensitivity of the basic reproductive number to the model's parameters. In the time-dependent control case, we use Pontryagin's maximum principle to derive necessary conditions for the optimal control of the disease. Finally, numerical simulations are performed to illustrate the analytical results. The cost-effectiveness analysis results show that optimal efforts on recruitment (HIV screening of applicants, etc.) is not the most cost-effective strategy to enhance productivity in the organizational labor force. Hence, to enhance employees' productivity, effective education programs and strict adherence to preventive measures should be promoted. [ABSTRACT FROM AUTHOR]

In this paper, a deterministic malaria transmission model in the presence of a drug-resistant strain is investigated. The model is studied using stability theory of differential equations, optimal control, and computer simulation. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved in the absence of a drug-resistant strain in the population. The existence of multiple endemic equilibria is also established. Both the Sensitivity Index (SI) of the model parameters and the Incremental Cost-Effectiveness Ratio (ICER) for all possible combinations of the disease-control measures are determined. Our results revealed among others that the most cost-effective strategy for drug-resistant malaria control is the combination of the provision of basic amenities (such as access to clean water, electricity, good roads, health care, and education) and treatment of infective individuals. Therefore, more efforts from policy-makers on the provisions of basic amenities and treatment of infectives would go a long way to combat the malaria epidemic. [ABSTRACT FROM AUTHOR]

Many financial optimization problems involve future values of security prices, interest rates and exchange rates which are not known in advance, but can only be forecast or estimated. Several methodologies have therefore, been proposed to handle the uncertainty in financial optimization problems. One such methodology is Robust Statistics, which addresses the problem of making estimates of the uncertain parameters that are insensitive to small variations. A different way to achieve robustness is provided by Robust Optimization which, given optimization problems with uncertain parameters, looks for solutions that will achieve good objective function values for the realization of these parameters in given uncertainty sets. Robust Optimization thus offers a vehicle to incorporate an estimation of uncertain parameters into the decision making process. This is true, for example, in portfolio asset allocation. Starting with the robust counterparts of the classical mean-variance and minimum-variance portfolio optimization problems, in this paper we review several mathematical models, and related algorithmic approaches, that have recently been proposed to address uncertainty in portfolio asset allocation, focusing on Robust Optimization methodology. We also give an overview of some of the computational results that have been obtained with the described approaches. In addition we analyse the relationship between the concepts of robustness and convex risk measures. [ABSTRACT FROM AUTHOR]

Spillover of trypanosomiasis parasites from wildlife to domestic livestock and humans remains a major challenge world over. With the disease targeted for elimination by 2030, assessing the impact of control strategies in communities where there are human-cattle-wildlife interactions is therefore essential. A compartmental framework incorporating tsetse flies, humans, cattle, wildlife and various disease control strategies is developed and analyzed. The reproduction is derived and its sensitivity to different model parameters is investigated. Meanwhile, the optimal control theory is used to identify a combination of control strategies capable of minimizing the infected human and cattle population over time at minimal costs of implementation. The results indicates that tsetse fly mortality rate is strongly and negatively correlated to the reproduction number. It is also established that tsetse fly feeding rate in strongly and positively correlated to the reproduction number. Simulation results indicates that time dependent control strategies can significantly reduce the infections. Overall, the study shows that screening and treatment of humans may not lead to disease elimination. Combining this strategy with other strategies such as screening and treatment of cattle and vector control strategies will result in maximum reduction of tsetse fly population and disease elimination. [ABSTRACT FROM AUTHOR]

Social balance theory describes allowable and forbidden configurations of thetopologies of signed directed social appraisal networks. In this paper, wepropose two discrete-time dynamical systems that explain how an appraisalnetwork \textcolor{blue}{converges to} social balance from an initiallyunbalanced configuration. These two models are based on two differentsocio-psychological mechanisms respectively: the homophily mechanism and theinfluence mechanism. Our main theoretical contribution is a comprehensiveanalysis for both models in three steps. First, we establish the well-posednessand bounded evolution of the interpersonal appraisals. Second, we fullycharacterize the set of equilibrium points; for both models, each equilibriumnetwork is composed by an arbitrary number of complete subgraphs satisfyingstructural balance. Third, we establish the equivalence among three distinctproperties: non-vanishing appraisals, convergence to all-to-all appraisalnetworks, and finite-time achievement of social balance. In addition totheoretical analysis, Monte Carlo validations illustrates how the non-vanishingappraisal condition holds for generic initial conditions in both models.Moreover, numerical comparison between the two models indicate that thehomophily-based model might be a more universal explanation for the formationof social balance. Finally, adopting the homophily-based model, we presentnumerical results on the mediation and globalization of local conflicts, thecompetition for allies, and the asymptotic formation of a single versus twofactions.

Zika virus is a flavivirus transmitted to humans primarily through the bite of infected Aedes mosquitoes. In addition to vector-borne spread, however, the virus can also be transmitted through sexual contact. In this paper, we formulate and analyze a new system of ordinary differential equations which incorporates both vector and sexual transmission routes. Theoretical analysis of this model when there is no disease induced mortality shows that the disease-free equilibrium is locally and globally asymptotically stable whenever the associated reproduction number is less than unity and unstable otherwise. However, when we extend this same model to include Zika induced mortality, which have been documented in Latin America, we find that the model exhibits a backward bifurcation. Specifically, a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. To further explore model predictions, we use numerical simulations to assess the importance of sexual transmission to disease dynamics. This analysis shows that risky behavior involving multiple sexual partners, particularly among male populations, substantially increases the number of infected individuals in the population, contributing significantly to the disease burden in the community. [ABSTRACT FROM AUTHOR]

This paper investigates a new model on coronavirus-19 disease (COVID-19) with three compartments including susceptible, infected, and recovered class under Mittag-Leffler type derivative. The mentioned derivative has been introduced by Atangana, Baleanu, and Caputo abbreviated as (ABC) . Upon utilizing fixed point theory, we first prove the existence of at least one solution for the considered model and its uniqueness. Also, some results about stability of Ulam–Hyers type are also established. By applying a numerical technique called fractional Adams–Bashforth (AB) method, we develop a scheme for the approximate solutions to the considered model. Using some real available data, we perform the concerned numerical simulation corresponding to different values of fractional order. [ABSTRACT FROM AUTHOR]

We propose a probabilistic enhancement of standard kernel Support VectorMachines for binary classification, in order to address the case when, alongwith given data sets, a description of uncertainty (e.g., error bounds) may beavailable on each datum. In the present paper, we specifically considerGaussian distributions to model uncertainty. Thereby, our data consist of pairs$(x_i,\Sigma_i)$, $i\in\{1,\ldots,N\}$, along with an indicator$y_i\in\{-1,1\}$ to declare membership in one of two categories for each pair.These pairs may be viewed to represent the mean and covariance, respectively,of random vectors $\xi_i$ taking values in a suitable linear space (typically$\mathbb R^n$). Thus, our setting may also be viewed as a modification ofSupport Vector Machines to classify distributions, albeit, at present, onlyGaussian ones. We outline the formalism that allows computing suitableclassifiers via a natural modification of the standard "kernel trick." The maincontribution of this work is to point out a suitable kernel function forapplying Support Vector techniques to the setting of uncertain data for which adetailed uncertainty description is also available (herein, "Gaussian points").

Corona virus disease 2019 (Covid-19) is an illness caused by a natural corona virus called severe acute respiratory syndromes corona virus 2 (SARS-COV-2 formally called Covid-19) which is respiratory illness and has been declared the Covid-19 outbreak a global pandemic by World Health Organization (WHO). Presently, Covid-19 becomes a health concern around the globe. In present article, we investigated the dynamics of Covid-19 infectious disease under the fractional order derivative from both theoretical as well as analytical aspects. Using fixed-point theory results, we developed the indispensable conditions for the existence of the solution of the proposed model. Further we have used the techniques of Laplace transform coupled with the Adomian's decomposition method to obtain the semi analytical solution for the model under consideration. Finally we have provided some graphical presentation corresponding to different fractional order derivatives via Matlab for the desired solutions. [ABSTRACT FROM AUTHOR]

With the continuous innovation of scientific research, technological level and social and economic development, the technological innovation of enterprises in the continuous management is also facing a new breakthrough and upgrade. Especially for enterprises in the era of big data, in order to better respond to the new demands of the development of the new era, enterprise managers should make effective technological innovation from the global economic growth trend on the basis of clarifying their own development advantages. Therefore, on the basis of understanding the multiple linear regression model and its construction conditions, this paper analyses the influencing variables in the actual development according to the current management technology and innovation of enterprises, and obtains the clear results of the model research.

The paper proposes a data model analysis algorithm for human motion function based on short-term behaviour. The algorithm uses a functional data analysis (FDA) method to perform Fourier fitting on the motion data and extract the fitted approximate single period data. Finally, the algorithm depicts the internal change in the motion in the low-dimensional space. The study found that the characteristic motion data obtained by the algorithm has smooth characteristics, and the relevant case analysis also verifies the algorithm's effectiveness.

To help people solve unsolved problems in everyday life and solve the complexity of life, this paper proposes an artificial intelligence algorithm and establishes a mathematical model for simulation experiments. The results show that the artificial intelligence algorithm can search the optimal solution in a short time, with a success rate of 95.87%. Under the same conditions, relative to other algorithms, it can not only improve the success rate of the optimal solution, but also the search solution has very significant advantages.