In this paper, numerical technique based on monic Laguerre polynomials is proposed to obtain approximate solutions of initial value problems for systems of fractional order integro-differential equations (FIDEs). Operational fractional integral matrix is constructed. This operational matrix is applied together with the monic Laguerre Tau method to solve systems of FIDEs. This systems of FIDEs will be transformed into a system of algebraic equations which can be solved easily. Numerical results and comparisons with other methods are also presented to show the efficiency and applicability of the proposed method.

In this work, we investigated a nonlinear two-term boundary value problem involving the $\psi$-Caputo fractional derivative with integral boundary conditions. By a construction of its associated Green function and application of the upper and lower solutions method together with some fixed point theorems due to Banach and Schauder, we established the existence and uniqueness of positive solutions of our considered main problem. At the end some illustrative examples are provided to validate our theoretical results.

In this paper, using a new identity, we study one of the famous Newton-Cotes three-point quadraturerules. More precisely Maclaurin’s quadrature rule, for which we establish the error estimate of this methodunder the constraint that the first derivatives belong to the class of preinvex functions. We also give someapplications to special means as applications. We believe that this new studied inequality and the resultsobtained in this article will further inspire intrigued researchers.

This paper focuses on the use of wolbachia to control the spread of zika virus disease. Zika virus disease is an arboviral disease that spreads through bites of female mosquitoes in the aedes family especially, aedes aegypti. Experimental studies have indicated that wolbachia could be used to prevent the spread of zika virus disease by infecting aedes aegypti with wolbachia in a laboratory and releasing them in the wild to mate with the wild aedes aegypti. A system of nonlinear ordinary differential equations is used to model the use of wolbachia to stop the spread of zika virus disease in the human and mosquito populations. as well as the population of wolbachia-infected aedes aegypti used as control. It is shown through bifurcation analysis that the model exhibits forward bifurcation, which confirms that a unique endemic equilibrium exists in the model when the control reproduction number, $ \mathcal{R}_c>1$. The existence of forward bifurcation in the model means that $ \mathcal{R}_c<1$ is enough to guarantee eradication of zika virus disease using wolbachia as a biocontrol. Hence, the spread of zika virus disease can be controlled irrespective of the initial sizes of infected human and mosquito populations

The aim of this paper is to define and emphasize a strong form of D-compact sets in generalized metricspaces, namely D-precompact sets. Also with other sets, we shall study the relationships. Furthermore, wegive the notions of sequentially D-precompact sets.

Analytical solution of thermo diffusion effect on magnetohydrodynamics flow of fractionalized Cassonfluid over a vertical plate immersed in a porous media is obtained. Moreover, in the model of the problem, additional effects, like a chemical reaction, heat source/sink, and thermal radiation are also considered.The model is solved by three approaches, namely, Atangana-Baleanu, Caputo-Fabrizio, and Caputo fractionalderivative of non-integer order γ. The governing dimensionless equations for temperatures, concentrations,and velocities are solved using Laplace transform method and compared graphically. The effects of different parameters like fractional parameter γ, Thermo diffusion Sr, and magnetic parameter M are discussedthrough numerous graphs. Furthermore, comparisons among ordinary and fractionalized velocity fields arealso drawn. It is found that the velocity obtained with Atangana-Baleanu fractional derivative is less than thatobtained by Caputo, Caputo-Fabrizio, or ordinary derivatives.

Corruption is a slow poison damaging students and consequently societies and nations, virtually, all students of Nigerian tertiary institutions are exposed to corruption. In this study, an attempt is made to formulate the dynamics of corruption among students of Nigerian tertiary institutions. We describe mathematical modeling of corruption among students using an epidemiological compartment model. The population at risk of adopting corrupt ideology was divided into four compartments: S(t) is the susceptible class, E(t) is the Exposed class, C(t) is the Corrupted class and P(t) is the punished class. The positivity and boundedness of the model were established. The model possesses both corruption-free and endemic equilibrium. Likewise, the model exhibits threshold dynamics characterized by the basic reproduction number R0. The numerical implementation of the model reveals that corruption will persist among Nigeria students if the root cause were not eradicated.

Kenya records over 1.5 million cases of HIV-infected people with a prevalence of 4.8% among adultsin 2019, ranking Kenya as the seventh-largest HIV population in the world. A recent study showed that55.9% of Kenyan truckers pay for sex in while 46.6% had a regular partner along their trucking route inaddition to a wife or girlfriend at home. The complexity in the sexual network of Truckers, which can be aconduit for the widespread of HIV, necessitated the need to better understand the dynamics of transmissionof HIV/AIDS between truckers and female sex workers. In this study, a model is formulated for HIV/AIDSdynamics along the Northern corridor highway in Kenya. The reproduction number, disease-free equilibriumand endemic equilibrium points were determined and their stabilities were also determined using the nextgenerationmatrix method. The disease-free equilibrium is stable when R0u < 1, R0c < 1 and R0f < 1 whilethe endemic equilibrium point is stable when R0u > 1, R0c > 1 and R0f > 1. It is found that circumcision canbe used as an intervention to minimize the infection of HIV among truckers and female sex workers.

In this paper we solve some fifth and sixth order boundary value problems (BVPs) by the improved residual power series method (IRPSM). IRPSM is a method that extends the residual power series method (RPSM) to (BVPs) without requiring exact solution. The presented method is capable to handle both linear and nonlinear boundary value problems (BVPs) effectively. The solutions provided by IRPSM are compared with the actual solution and with the existing solutions. The results demonstrate that the approach is extremely accurate and dependable.

Positive maps are essential in the description of quantum systems. However, characterization of the structure of the set of all positive maps is a challenge in mathematics and mathematical physics. We construct a linear positive map from M4 to M5 and state the conditions under which they are positive and completely positive (copositivity of positive).