Since certain species of domestic poultry and poultry are the main food source in many countries, the outbreak of avian influenza, such as H7N9, is a serious threat to the health and economy of those ...countries. This can be considered as the main reason for considering the preventive ways of avian influenza. In recent years, the disease has received worldwide attention, and a large variety of different mathematical models have been designed to investigate the dynamics of the avian influenza epidemic problem. In this paper, two fractional models with logistic growth and with incubation periods were considered using the Liouville-Caputo and the new definition of a nonlocal fractional derivative with the Mittag-Leffler kernel. Local stability of the equilibria of both models has been presented. For the Liouville-Caputo case, we have some special solutions using an iterative scheme via Laplace transform. Moreover, based on the trapezoidal product-integration rule, a novel iterative method is utilized to obtain approximate solutions for these models. In the Atangana-Baleanu-Caputo sense, we studied the uniqueness and existence of the solutions, and their corresponding numerical solutions were obtained using a novel numerical method. The method is based on the trapezoidal product-integration rule. Also, we consider fractal-fractional operators to capture self-similarities for both models. These novel operators predict chaotic behaviors involving the fractal derivative in convolution with power-law and the Mittag-Leffler function. These models were solved numerically via the Adams-Bashforth-Moulton and Adams-Moulton scheme, respectively. We have performed many numerical simulations to illustrate the analytical achievements. Numerical simulations show very high agreement between the acquired and the expected results.
•Discussing the Hyers-Ulam stability for nonlinear differential equations involving Atangana-Baleanu fractional derivatives.•Fractional differential equations with singularity and nonlinear ...p-Laplacian operator in Banach’s space are studied.•Guo-Krasnoselskii theorem was consider to obtain the results.
In this paper we are established the existence of positive solutions (EPS) and the Hyers-Ulam (HU) stability of a general class of nonlinear Atangana-Baleanu-Caputo (ABC) fractional differential equations (FDEs) with singularity and nonlinear p-Laplacian operator in Banach’s space. To find the solution for the EPS, we use the Guo-Krasnoselskii theorem. The fractional differential equation is converted into an alternative integral structure using the Atangana-Baleanu fractional integral operator. Also, HU-stability is analyzed. We include an example with specific parameters and assumptions to show the results of the proposal.
Abstract
The current study presents a novel application of integrated intelligent computing solver for numerical treatment of second‐order prediction differential models by exploiting the continuous ...mapping of artificial neural network (ANN) models of differential operators, global/local search optimization competencies of combined genetic algorithms (GAs) and sequential quadratic programming (SQPs), that is, ANNGASQP. Neural network based differential models are arbitrary integrated to formulate merit function in mean squared error sense and merit function globally optimized with GAs aided with local refinements of SQP. The integrated neuro‐evolutionary ANNGASQP scheme is implemented on four different numerical examples of the prediction differential models for numerical solution to examine the precision, proficiency, and consistency. The comparison of proposed solutions through ANNGASQP for prediction differential models with available reference results indicate the good agreement with absolute errors around 10
−6
to 10
−8
. The worth of ANNGASQP is further established through near optimal values of performance measures on statistical date for multiple trials.
•A comparative and chaotic study of tumor and effector cells through fractional tumor-immune dynamical model was investigated.•Performance was done using the strategy of Adams-Bashforth-Moulton and ...Toufik-Atangana methods.•The existence and uniqueness of the given tumor-immune model of arbitrary order are analyzed.
A tumor is most dangerous disease of medical science which is a mass or lumps of tissue that’s formed by an accumulation of abnormal cells. A famous fractional tumor-immune model is interpreting the dynamics of tumor and effector cells. In this work, we provide a comparative and chaotic study of tumor and effector cells through fractional tumor-immune dynamical model. A new arbitrary operator based on the Mittag-Leffler law is assumed for this study. Again, we examine the interactions among distinct tumor cell inhabitants and immune structure through a model of real world problem of medical science. We First investigate the dynamical effect of the activation of the effector immune and tumor cells by using Adams-Bashforth-Moulton and Toufik-Atangana methods. Furthermore, this paper analyses the existence and uniqueness of given tumor-immune model of arbitrary order. Further, we have examined the dynamical behaviors of the fractional tumor-immunne model and obtained results are compared with exiting results by other methods. Numerical simulations are executed by Adams-Bashforth-Moulton and Toufik-Atangana methods using popular Atangana-Baleanu fractional derivative. Our obtained results will be useful for biologists to the treatment of cancer disease.
Honey bee decline is currently one of the world's most serious environmental issues, and scientists, governments, and producers have generated interest in understanding its causes and consequences in ...honey production and food supply. Mexico is one of the world's top honey producers, however, the honey bee population's status has not been documented to date. Based on 32 years of data from beekeeping, we make a country-level assessment of honey bee colony trends in Mexico. We use generalized additive mixed models to measure the associations between the percent change in honey bee hives and the percent change in honey yield per hive in relation to land-use, climate, and socioeconomic conditions. Despite the fact that the average annual yield per hive increased from 1980 to 2012, we detected a significant decline in the percent change in the number of honey bee hives across the time period studied. We also found a relationship between climatic conditions and agricultural land use, with agriculture increases and high temperatures producing a decrease in the percent change in honey yield. We found a relationship between a reduction in the temperature range (the difference between maximum and minimum temperatures) and a decrease in the percent change in the number of hives, while socioeconomic factors related to poverty levels have an impact on the number of hives and honey yields. Although long-term declines in hive numbers are not correlated with poverty levels, socioeconomic factors in states with high and medium poverty levels limit the increase in honey yield per hive. These results provide evidence that land-use changes, unfavorable climatic conditions, political, and socioeconomic factors are partially responsible for the reductions in the percent change in honey bee hives in Mexico.
New approach of fractional derivative with a new local kernel is suggested in this paper. The kernel introduced in this work is the well-known normal distribution that is a very common continuous ...probability distribution. This distribution is very important in statistics and also highly used in natural science and social sciences to portray real-valued random variables whose distributions are not known. Two definitions are suggested namely Atangana–Gómez Averaging in Liouville–Caputo and Riemann–Liouville sense. We presented some relationship with existing integrals transform operators. Numerical approximations for first and second order approximation are derived in detail. Some Applications of the new mathematical tools to describe some real world problems are presented in detail. This is a new door opened the field of statistics, natural and socials sciences.
•New differential operator was constructed using the normal distribution as kernel.•A new integral operator has been obtained.•Relations of new operators and existing integrals transform have been established.•The numerical approximation of the new operators has been suggested.•The new operators were applied to model three real world problems.
Thermal convection suppresses the thermal stability and instability during the interaction between the magnetic fields because thermal convection is the most significant driver of time-dependent ...patterns of motion within magnetized and non-magnetized chaotic. In this manuscript, a mathematical modeling is proposed subject to the magnetohydrodynamic conductive fluid lying on an infinite horizontal layer subject to heat from below with gravity. The mathematical model is based on nonlinear ordinary differential equations and such model has been investigated by means of the Boussinesq approximation and Darcy's law. The newly defined techniques of fractal–fractional differential operators, namely Atangana–Baleanu and Caputo–Fabrizio fractal–fractional differentiations, have been imposed on the governing equations. The mathematical analysis based on the equilibrium points and stability criteria is investigated to examine the dynamic responses of a magnetized and non-magnetized conductive fluid model. The numerical simulations have been performed by Adams methods, which is so-called the explicit scheme of the Adams–Bashforth method. Our results suggest that the comparative evolution of trajectories between magnetized and non-magnetized chaotic behaviors has strong effects due to Lorentz force that showed the resistivity in chaotic phenomenon.
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•Postbiotics and paraprobiotics denote the health benefits beyond probiotic viability.•Postbiotics and paraprobiotics possess protective effect in cell lines/animal models.•More human ...trials are needed to support their effectiveness and health claims.•Postbiotics and paraprobiotics may contribute to the improvement of host health.
In recent years, new probiotic-related concepts such as postbiotics and paraprobiotics have been used to describe non-viable microorganisms or bacterial-free extracts that may provide benefits to the host by offering bioactivities additional to probiotics. However, several aspects related to these postbiotics and paraprobiotics bioactivities remain unexplored or are poorly understood. Therefore, the aim of this work is to provide an overview of the general aspects and emerging trends of postbiotics and paraprobiotics, such as conceptualization of terms, production, characterization, bioactivities, health-promoting effects, bioengineering approaches, and applications. In vitro and in vivo studies have demonstrated that some postbiotics and paraprobiotics exhibit bioactivities such as anti-inflammatory, immunomodulatory, anti-proliferative, antioxidant, and antimicrobial. These bioactivities could be involved in health-promoting effects observed in human and clinical trials, but despite the scientific evidence available, the mechanisms of action and the signaling pathways involved have not been fully elucidated. Nevertheless, paraprobiotics and postbiotics possess valuable potential for the development of biotechnological products with functional ingredients for the nutraceutical industry.
The biological models for the study of human immunodeficiency virus (HIV) and its advanced stage acquired immune deficiency syndrome (AIDS) have been widely studied in last two decades. HIV virus can ...be transmitted by different means including blood, semen, preseminal fluid, rectal fluid, breast milk, and many more. Therefore, initiating HIV treatment with the TB treatment development has some advantages including less HIV‐related losses and an inferior risk of HIV spread also having difficulties including incidence of immune reconstitution inflammatory syndrome (IRIS) because of a large pill encumbrance. It has been analyzed that patients with HIV have more weaker immune system and are susceptible to infections, for example, tuberculosis (TB). Keeping the importance of the HIV models, we are interested to consider an analysis of HIV‐TB coinfected model in the Atangana‐Baleanu fractional differential form. The model is studied for the existence, uniqueness of solution, Hyers‐Ulam (HU) stability and numerical simulations with assumption of specific parameters.
