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AbstractIn this article, a new approach to study the fractionalized second grade fluid flow is described by the different fractional derivative operators near an exponentially accelerated vertical plate together with exponentially variable velocity, energy and mass diffusion through a porous media is critically examined. The phenomenon has been expressed in terms of partial differential equations, then transformed the governing equations in non-dimentional form. For the sake of better rheology of second grade fluid, developed a fractional model by applying the new definition of Constant Proportional-Caputo hybrid derivative (CPC), Atangana Baleanu in Caputo sense (ABC) and Caputo Fabrizio (CF) fractional derivative operators that describe the generalized memory effects. For seeking exact solutions in terms of Mittag-Leffler and G-functions for velocity, temperature and concentration equations, Laplace integral transformation technique is applied. For physical significance of various system parameters on fluid velocity, concentration and temperature distributions are demonstrated through various graphs by using graphical software. Furthermore, for being validated the acquired solutions, accomplished a comparative analysis with some published work. It is also analyzed that for exponential heating and non-uniform velocity conditions, the CPC fractional operator is the finest fractional model to describe the memory effect of velocity, energy and concentration profile. Moreover, the graphical representations of the analytical solutions illustrated the main results of the present work. Also, in the literature, it is observed that to derived analytical results from fractional fluid models developed by the various fractional operators, is difficult and this article contributing to answer the open problem of obtaining analytical solutions the fractionalized fluid models.

Abstract The subject of the article is devoted to the development of a matrix collocation technique based upon the combination of the fractional-order shifted Vieta–Lucas functions (FSVLFs) and the quasilinearization method (QLM) for the numerical evaluation of the fractional multi-order heat conduction model related to the human head with singularity and nonlinearity. The fractional operators are adopted in accordance with the Liouville–Caputo derivative. The quasilinearization method (QLM) is first utilized in order to defeat the inherent nonlinearity of the problem, which is converted to a family of linearized subequations. Afterward, we use the FSVLFs along with a set of collocation nodes as the zeros of these functions to reach a linear algebraic system of equations at each iteration. In the weighted $$L_2$$ L 2 norm, the convergence analysis of the FSVLFs series solution is established. We especially assert that the expansion series form of FSVLFs is convergent in the infinity norm with order $${\mathcal {O}(\frac{1}{K^3})}$$ O ( 1 K 3 ) , where K represents the number of FSVLFs used in approximating the unknown solution. Diverse computational experiments by running the presented combined QLM-FSVLFs are conducted using various fractional orders and nonlinearity parameters. The outcomes indicate that the QLM-FSVLFs produces efficient approximate solutions to the underlying model with high-order accuracy, especially near the singular point. Furthermore, the methodology of residual error functions is employed to measure the accuracy of the proposed hybrid algorithm. Comparisons with existing numerical models show the superiority of QLM-FSVLFs, which also is straightforward in implementation.

The objective of this study was to assess the water quality status of the surface water and groundwater resources in the Middelburg area, South Africa. The assessment was addressed using combined water quality indices, investigating selected chemical parameters over four different seasons for a period of five years from 2017 to 2021. A combination of the Canadian Council of Ministers of the Environment water quality index and the comprehensive pollution index was used to analyze the water quality status of surface water and groundwater of the town of Middelburg, situated near coal mining activities in Mpumalanga, South Africa. The combination of the indices indicated that some surface water monitoring sites ranged between poor to fair water quality. Groundwater monitoring points also showed a poor to fair ranking. The comprehensive pollution index confirmed that some sites showed very poor water quality in the summer seasons, exceeding expected limits for the period 2017 to 2021. The principal component analysis further showed that both surface water and groundwater sites had high levels of contamination with increased chemical parameters. The results were compared against the different water quality guidelines. In an extensive monitoring program, water management systems must be properly implemented to mitigate impacts on water resources.

Abstract The present work examines the analytical solutions of the double duffusive magneto free convective flow of Oldroyd-B fluid model of an inclined plate saturated in a porous media, either fixed or moving oscillated with existence of slanted externally magnetic field. The phenomenon has been expressed in terms of partial differential equations, then transformed the governing equations in non-dimensional form. On the fluid velocity, the influence of different angles that plate make with vertical is studied as well as slanted angles of the electro magnetic lines with the porous layered inclined plate are also discussed, associated with thermal conductivity and constant concentration. For seeking exact solutions in terms of special functions namely Mittag–Leffler functions, G-function etc., for Oldroyd-B fluid velocity, concentration and Oldroyd-B fluid temperature, Laplace integral transformation method is used to solve the non-dimensional model. The contribution of different velocity components are considered as thermal, mass and mechanical, and analyse the impacts of these components on the fluid dynamics. For several physical significance of various fluidic parameters on Oldroyd-B fluid velocity, concentration and Oldroyd-B fluid temperature distributions are demonstrated through various graphs. Furthermore, for being validated the acquired solutions, some limiting models such as Newtonian fluid in the absence of different fluidic parameters. Moreover, the graphical representations of the analytical solutions illustrated the main results of the present work and studied various cases regarding the movement of plate.

A new approach to investigates the analytical solutions of the mathematical fractional Casson fluid model that is described by the Yang-Abdel-Cattani fractional operator having Rabotnov exponential kernel near an infinitely vertical plate. The phenomenon has been expressed in terms of partial differential equations, then transformed the governing equations in non-dimentional form. For the sake of better rheology of Casson fluid, developed a fractional model by applying the new definition of Yang-Abdel-Cattani fractional derivative operator having Rabotnov exponential kernel that describe the generalized memory effects. For seeking exact solutions in terms of Mittag-Leffler functions, for fluid velocity, concentration and temperature, Laplace integral transformation method is used to solve the fractional model. For several physical significance of various fluid parameters such as α, β, Pr, Gr, Gm, Sc on velocity, concentration and temperature distributions are demonstrated through various graphs and it is noticed that the Yang-Abdel-Cattani fractional parameter portrayed the retardation effect on momentum and energy profile, but it is visualized that for small values of Casson fluid parameter the velocity profile is higher. Furthermore, for being validated the acquired solutions, some limiting models such as ordinary Newtonian model had recovered from Yang-Abdel-Cattani fractional Casson fluid. Moreover, the graphical representations of the analytical solutions illustrated the main results of the present work. Also, in the literature, it is observed that to derived analytical results from fractional fluid models developed by the various fractional operators, is difficult and this article contributing to answer the open problem of obtaining analytical solutions the fractionalized fluid models.

Using some investigations based on information theory, the model proposed by Keller and Segel was extended to the concept of fractional derivative using the derivative with fractional order without singular kernel recently proposed by Caputo and Fabrizio. We present in detail the existence of the coupled-solutions using the fixed-point theorem. A detailed analysis of the uniqueness of the coupled-solutions is also presented. Using an iterative approach, we derive special coupled-solutions of the modified system and we present some numerical simulations to see the effect of the fractional order.

The model of population growth is revised in this paper. A new model is proposed based on the concept of fractional differentiation that uses the generalized Mittag-Leffler function as kernel of differentiation. The new model includes the choice of sexuality. The existence of unique solution is investigated and numerical solution is provided.

In recent years the world has witnessed the arrival of deadly infectious diseases that have taken many lives across the globe. To fight back these diseases or control their spread, mankind relies on modeling and medicine to control, cure, and predict the behavior of such problems. In the case of Ebola, we observe spread that follows a fading memory process and also shows crossover behavior. Therefore, to capture this kind of spread one needs to use differential operators that posses crossover properties and fading memory. We analyze the Ebola disease model by considering three differential operators, that is the Caputo, Caputo–Fabrizio, and the Atangana–Baleanu operators. We present brief detail and some mathematical analysis for each operator applied to the Ebola model. We present a numerical approach for the solution of each operator. Further, numerical results for each operator with various values of the fractional order parameter α are presented. A comparison of the suggested operators on the Ebola disease model in the form of graphics is presented. We show that by decreasing the value of the fractional order parameter α , the number of individuals infected by Ebola decreases efficiently and conclude that for disease elimination, the Atangana–Baleanu operator is more useful than the other two.

Unlike issues in biomedical research ethics, ethical challenges arising in daily clinical care in Sub-Saharan African countries have not yet been studied in a systematic manner. However this has to be seen as a distinct entity as we argue in this paper. Our aim was to give an overview of the spectrum of clinical ethical issues and to understand what influences clinical ethics in the Sub-Saharan country of Gabon.In-depth interviews with 18 health care professionals were conducted at three hospital sites in Gabon. Interview transcripts were analyzed using a grounded theory approach (open and axial coding), giving a qualitative spectrum of categories for clinical ethical issues. Validity was checked at a meeting with study participants and other health care experts in Gabon after analysis of the data.Twelve main categories (with 28 further-specified subcategories) for clinical ethical issues were identified and grouped under three core categories: A) micro level: "confidentiality and information", "interpersonal, relational and behavioral issues", "psychological strain of individuals", and "scarce resources"; B) meso level: "structural issues of medical institutions", "issues with private clinics", "challenges connected to the family", and "issues of education, training and competence"; and C) macro level: "influence of society, culture, religion and superstition", "applicability of western medicine", "structural issues on the political level", and "legal issues".Interviewees reported a broad spectrum of clinical ethical issues that go beyond challenges related to scarce financial and human resources. Specific socio-cultural, historical and educational backgrounds also played an important role. In fact these influences are central to an understanding of clinical ethics in the studied local context. Further research in the region is necessary to put our study into perspective. As many participants reported a lack of awareness of ethical issues amongst other health care professionals in daily clinical practice, we suggest that international organizations and national medical schools should consider infrastructure and tools to improve context-sensitive capacity building in clinical ethics for Sub-Saharan African countries like Gabon.

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

The Vallis model for El Niño is an important model describing a very interesting physical problem. The aim of this paper is to investigate and compare the models using both integer and non-integer order derivatives. We first studied the model with the local derivative by presenting for the first time the exact solution for equilibrium points, and then we presented the exact solutions with the numerical simulations. We further examined the model within the scope of fractional order derivatives. The fractional derivatives used here are the Caputo derivative and Caputo–Fabrizio type. Within the scope of fractional derivatives, we presented the existence and unique solutions of the model. We derive special solutions of both models with Caputo and Caputo–Fabrizio derivatives. Some numerical simulations are presented to compare the models. We obtained more chaotic behavior from the model with Caputo–Fabrizio derivative than other one with local and Caputo derivative. When compare the three models, we realized that, the Caputo derivative plays a role of low band filter when the Caputo–Fabrizio presents more information that were not revealed in the model with local derivative.

Information theory is used in many branches of science and technology. For instance, to inform a set of human beings living in a particular region about the fatality of a disease, one makes use of existing information and then converts it into a mathematical equation for prediction. In this work, a model of the well-known river blindness disease is created via the Caputo and beta derivatives. A partial study of stability analysis was presented. The extended system describing the spread of this disease was solved via two analytical techniques: the Laplace perturbation and the homotopy decomposition methods. Summaries of the iteration methods used were provided to derive special solutions to the extended systems. Employing some theoretical parameters, we present some numerical simulations.