Exact solutions of fractional evolution equations in the sense of Caputo-Hadamard with Cauchy and boundary conditions are obtained by employing the SBA method.

In this paper, we construct exact analytical solutions, where they exist, of some nonlinear fractional Schrödinger equations in the sense of Caputo-Hadamard. Our results are obtained using an improved version of the SBA method.

Human health is constantly threatened by the appearance and resurgence of several diseases, as shown by recent epidemics. COVID-19 was one of the epidemics that left its mark on the world in terms of economic and human damages. In the search for solution to this pandemic, the scientific community is involved in all its diversity. Mathematicians are taking part in the fight through mathematical modeling in various approaches. Ordinary derivative compartmental modeling approache is one of the techniques widely used in epidemiological modeling. This paper presents a mathematical contribution to fight against COVID-19 using a compartmental SQEICRS model. This model takes into account five stages. In particular, the role of chronic diseases on the dynamique of COVID-19, is focused. A mathematical analysis of the model has been carried out, and shows that the model is well-posed in the biological and mathematical sense. Aspects such as existence, equilibrium points and their stability, the basic reproduction number R0and sensitivity anlysis have been discussed. Sensitivity analysis allowed us to identify the parameters which contribute to the spread of the disease, including the chronicity rate due to chronic diseases. The direction of disease propagation was also determined according to R0. Finally, the numerical results with Matlab are in conformity with theoretical results.

In this paper, we have solved some time fractional Schr & ouml;dinger equations of order alpha with 0 < alpha <= 1 in dimension 1, 2 or 3 in the sense of Caputo by the SBA plus method. This method is based on two principles (successive approximations, and Picard) and the Adomian method. Secondly, it uses a process of rapid convergence in the functional space of the problem posed towards the exact solution, if it exists.

Elections are the heart of democracy. The choices made by a social group generally affect all the individuals in that group. So social choice is about the selection of options by a group of individuals. Many voting methods exist in the literature but these methods are not necessarily adapted to the situation of low-income countries, forcing these countries to go into debt to organize elections that sometimes do not express the will of the people. In our case we seek to elect a president of the republic by indirect suffrage. To do this we first organize a coupled election (legislative and municipal) in which mayors and deputies are elected. Then, the latter will in turn constitute the electors responsible for designating a president of the republic. The weight of the votes of these electors in the choice of the president is therefore a function of the schooling rate of the region where they were designated. Thus, by applying the vote by score and considering the weight of the votes of the electors, a winner is designated. The winner of the election is the one who obtains the most points. This voting method has the advantage of being less costly.

In this paper, we solve fractional time Navier-Stokes equations of order a in the Riemann-Liouville sense by a numerical method called Some Blaise Abbo (SBA) plus. The SBA plus uses an algorithm that converges faster to the exact solution, when it exists in the functional space of the problem. Received: March 8, 2023Revised: May 5, 2023

A deterministic model is formulated to describe the dynamics of malaria transmission using mosquito population and human population structured by immune status. The variation in mortality of humans and mosquitoes due to causes other than malaria, the infectiousness of recovered humans, the decay of acquired immunity and the immune system boosting are taken into account. The existence of biological meaningful solutions has been analyzed and a single disease-free equilibrium has been identified. The basic reproduction number is expressed in terms of the parameters of the model. The stability of the disease-free equilibrium has been analyzed. We have provided some basic conditions in which the disease dies out or persists. The numerical results showed the impact of immunity decay and immune system boosting on malaria transmission. Received: July 31, 2023Accepted: September 26, 2023

In this paper we have solved some temporal fractional functional equations in the sense of Caputo by a numerical method called SOME BLAISE ABBO(SBA). Unlike classical numerical methods, this method bypasses discretization. Despite its youth, it has already proven itself. Indeed, its accuracy and efficiency have already been proven in the solution of ODEs and PDEs with integer derivative. Its application to fractional functional equations constitutes an important scientific contribution. On the one hand, we demonstrate the efficiency of the SBA method to find exact solutions, when they exist, of some rather complicated problems, due to their nonlinearity. On the other hand, through these results, we bring essential information allowing the analysis of a given phenomenon in order to help the best decision making.

Voting plays a vital role in any society. Indeed the votes involve decision making especially and the more in the decision of group. Thanks to the opinions expressed by a group of people, an opinion representing the preference of the group is determined. But most often some voting methods seem to distance the result from a vote of the general opinion. The study of voting methods is based on the theory of social choice. For several years, in the literature on the theory of social choice, many theorists have contributed trying to find a representative voting method.It seems that there is no totally satisfactory way of voting.Thus we have tried, through this article, to design a voting method based on approval voting and the arithmetic mean that leads to goodcompromise results.In contrast to the other methods, the new method takes into account the choice of each voter and allows to obtain a result which represents the choice of the majority of the voters.

In this work, we have proposed some variants of MOMA-Plus method that we have numerically tested for the resolution of nonlinear multiobjective optimization problems. This MOMA-Plus method and variants differ from each other by the choice of aggregation functions in order to reduce the number of objective functions. The theoretical results allowing us to use these aggrega-tion functions to transform multiobjective optimization problems into single objective optimization problems are proved by two theorems. This study has highlighted the advantages of each aggre-gation function according to the type of Pareto front of the optimization problem. Six benchmarks test problems have been solved in this work by each of these methods and a comparative study was carried out through the performance indicators which are the differentiation with Pareto front, the convergence to the Pareto front and distributivity on the Pareto front. This allowed us to classify these methods on these benchmarks by using the Graphical Analysis for Interactive Assistance (GAIA) method.

 In this paper we have conceived an original deterministic model for the propagation of Covid-19 dynamics. Mathematical analysis of the model has been done and reveals the existence of a single disease-free equilibrium witch is locally and asymptotically stable. The basic reproduction number  has also been evaluated and gives an idea on the disease evolution in the world. This is because if , the disease disappears whereas if , the disease remains in the population. Numerical results are consistent with the theoretical results and highlight the effect of the infectious contact rate α on the evolution of the pandemic.Â

TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) is a very practical decision support method used in several areas of life. This method already exists in the literature in the context of a single decision maker. In order to adapt this method to group decision making, which can be easily applied in various situations, this work extended the TOPSIS method to group decision making using the quadratic mean and the geometric mean. In this work, numerical applications have been made and interesting results have been obtained.

In this paper, we use the SBA method to solve adaptive wave models for options pricing. This method consists to determine the solution in the form of converging series, if possible. The SBA method was applied with success because it has provided the exact solution to the problem.

Group decision-making plays a crucial role in decision support. Indeed today, it seems that a decision made by a single decision-maker hardly reflects reality. Many methods have been dealt with in group decision support. Generally, this is done through a collective aggregation function which, through the judgments given by each decision-maker on actions, must at the end find an action that is the best or represents a consensus. In many cases, the individual transformation into a collective preference encounters difficulties taking into account the fact that the use of certain methods generates a lot of calculations. Others are also based on the weighted average which is criticized because the weak criteria are compensated by the strongest. In this work, the collective aggregation function that we have developed is based on the quadratic mean. We note that it is easy to implement and does not entail compensation for the so-called weak criteria by the stronger ones. We also made a digital application and got some interesting results.

Social choice theory includes the study of voting methods. In the literature on social choice theory many methods exist, the main objective of all these methods is the determination of a good method. However, many of these methods give controversial results which often lead to disputes. It should also be noted that sometimes, regardless of the method used, there are people who are not ready to accept the results given by the ballot box. The ideal would be to find a method with good properties, because it seems that there are no completely satisfactory methods. Since the goal of a voting method is to reconcile several points of view into a general interest, one should focus on the properties. The geometric mean does not lead to a compensation of weak criteria by stronger ones as it is the case with the arithmetic mean. Indeed, by using the geometric mean, even if only one criterion is very weak and the others are very strong, a candidate may not be well ranked; moreover, assent voting is very well appreciated in the literature by many authors and also generates huge opportunities. This justifies our choice in this work to combine geometric mean and assent voting to develop a method with good properties.

In the literature on multi-criteria group decision support, many methods have been discussed. In general, these methods are based on collective aggregation functions that, through the judgments given by each decision maker on the actions according to each criterion, must determine an action that is the best or that represents a consensus. In some cases, the application of these methods is either complicated in use and others can also generate controversial results because of the weighted average they use. The objective of this work is to propose a new non-compensatory multi-criteria group decision support method that can circumvent some of these difficulties. The design of the latter consists in transforming a multi-decider problem into a single-decider problem using the geometric mean for the performance of the alternatives with respect to the criteria and the median for the criteria in order to use the ELECTRE I method within the framework of a single decision maker. The application of the new method and its comparison with other methods in the literature shows us that it has interesting properties.