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).

Let $X$ be a topological space and $\Omega \subset X$. Suppose $f:\Omega\rightarrow X$ is a function defined in a complete space $ \Omega $ and $ \tau $ is a vector in $ \mathbb{R} $ taking values in $X$. Suppose $ f $ is ap-Sequential Henstock integrable with respect to $\tau$, is $ f $ ap-Sequential Topological Henstock integrable with respect to $\tau$? It is the purpose of this paper to proffer affirmative answer to this question.

In this present case, we focus and explore the idea of a new family of convex function namely exponentialtype m–convex functions. To support this newly introduced idea, we elaborate some of its nice algebraicproperties. Employing this, we investigate the novel version of Hermite–Hadamard type integral inequality.Furthermore, to enhance the paper, we present several new refinements of Hermite–Hadamard (H−H) inequality.Further, in the manner of this newly introduced idea, we investigate some applications of specialmeans. These new results yield us some generalizations of the prior results in the literature. We believe, themethodology investigated in this paper will further inspire intrigued researchers.

When a pandemic occurs, it can cost fatal damages to human life. Therefore, it is important to understand the dynamics of a global pandemic in order to find a way of prevention. This paper contains an empirical study regarding the dynamics of the current COVID-19 pandemic. We have formulated a dynamic model of COVID-19 pandemic by subdividing the total population into six different classes namely susceptible, asymptomatic, infected, recovered, quarantined, and vaccinated. The basic reproduction number corresponding to our model has been determined. Moreover, sensitivity analysis has been conducted to find the most important parameters which can be crucial in preventing the outbreak. Numerical simulations have been made to visualize the movement of population in different classes and specifically to see the effect of quarantine and vaccination processes. The findings from our model reveal that both vaccination and quarantine are important to curtail the spread of COVID-19 pandemic. The present study can be effective in public health sectors for minimizing the burden of any pandemic.

Anemia, a global health problem, is increasing worldwide and affecting both developed and developingcountries. Being a blood disorder, anemia may occur in any stages of life but it is quite common in childrenunder the age of five. Globally, iron deficiency is the supreme contributor towards the onset of anemia. In thispaper, a general model based on the dynamics of anemia among children under five is formulated. The populationis divided in three classes such as susceptible, affected and treated. A time-dependent control measurenamely campaign program is considered. The model has an equilibrium point and the stability of the pointis analyzed. Moreover, sensitivity of the equilibrium point is also performed to discover the critical parameters.Numerical simulations are carried out to observe the dynamic behavior of the model. Results showthat campaign program is effective in minimizing the disease progression. The number of child patients andyearly deaths significantly decrease with accelerated campaign program that is implemented earlier whereastermination of the applied measure may upturn the burden. Findings also reveal that application of controlmeasure helps to reduce the prevalence of anemia but may not eliminate the disease.

In this paper, we study the relationship between Cartan's second curvature tensor $P_{jkh}^{i}$ and $(h) hv-$torsion tensor $C_{jk}^{i}$ in sense of Berwald. Moreover, we discuss the necessary and sufficient condition for some tensors which satisfy a recurrence property in $BC$-$RF_{n}$, $P2$-Like-$BC$-$RF_{n}$, $P^{\ast }$-$BC$-$RF_{n}$ and $P$-reducible-$BC-RF_{n}$.

The paper is concerned with stochastic random impulsive integro-differential equations with non-local conditions. The sufficient conditions guarantees uniqueness of mild solution derived using Banach fixed point theorem. Stability of the solution is derived by incorporating Banach fixed point theorem with certain inequality techniques.

In this paper, we define and investigate generalized exponential type convex functions namely exponentially $s$--convex function. In the support of this newly introduced idea, we attain the algebraic properties of this function, and furthermore, in the frame of simple calculus, we explore and attain the novel kind of Ostrowski type inequalities.

In this paper, we use a model of non-Newtonian second grade fluid which having three partial differentialequations of momentum, heat and mass transfer with initial condition and boundary condition. Wedevelop the modified Laplace transform of this model with fractional order generalized Caputo fractional operator.We find out the solutions for temperature, concentration and velocity fields by using modified Laplacetransform and investigated the impact of the order α and ρ on temperature, concentration and velocity fieldsrespectively. From the graphical results, we have seen that both the α and ρ have reverse effect on the fluidflow properties. In consequence, it is observed that flow properties of present model can be enhanced nearthe plate for smaller and larger values of ρ. Furthermore, we have compared the present results with theexisting literature for the validation and found that they are in good agreement.

We introduce and study some properties of fuzzy Henstock-Kurzweil-Stietljes-$ \Diamond $-double integral on time scales. Also, we state and prove the uniform convergence theorem, monotone convergence theorem and dominated convergence theorem for the fuzzy Henstock-Kurzweil Stieltjes-$\Diamond$-double integrable functions on time scales.

In this paper, the authors introduced a novel definition based on Hilfer fractional derivative, which name $q$-Hilfer fractional derivative of variable order. And the uniqueness of solution to $q$-Hilfer fractional hybrid integro-difference equation of variable order of the form \eqref{eq:varorderfrac} with $0 < \alpha(t) < 1$, $0 \leq \beta \leq 1$, and $0 < q < 1$ is studied. Moreover, an example is provided to demonstrate the result.

In this work, we investigate a modified population model of non-infected and infected (SI) compartmentsto predict the spread of the infectious disease COVID-19 in Pakistan. For Approximate solution, we use LaplaceAdomian Decomposition Method (LADM). With the help of the said technique, we develop an algorithmto compute series type solution to the proposed problem. We compute few terms approximate solutionscorresponding to different compartment. With the help of MATLAB, we also plot our approximate solutionsfor different compartment graphically.

The aim of this paper is to study the F-contraction mapping introduced by Wardowski to obtain fixed point results by method of Samet in generalized complete metric spaces. Our findings extend the results announced by Samet methods and some other works in generalized metric spaces.

This research is devoted to studying a class of implicit fractional order differential equations ($\mathrm{FODEs}$) under anti-periodic boundary conditions ($\mathrm{APBCs}$). With the help of classical fixed point theory due to $\mathrm{Schauder}$ and $\mathrm{Banach}$, we derive some adequate results about the existence of at least one solution. Moreover, this manuscript discusses the concept of stability results including Ulam-Hyers (HU) stability, generalized Hyers-Ulam (GHU) stability, Hyers-Ulam Rassias (HUR) stability, and generalized Hyers-Ulam- Rassias (GHUR)stability. Finally, we give three examples to illustrate our results.

The main aim of this paper is to clarify the action of the discrete Laplace transform on the fractional proportional operators. First of all, we recall the nabla fractional sums and differences and the discrete Laplace transform on a time scale equivalent to $h\mathbb{Z}$. The discrete $h-$Laplace transform and its convolution theorem are then used to study the introduced discrete fractional operators.

In this paper, we establish a fixed point theorem for controlled rectangular $b-$metric spaces for mappings that satisfy $(\psi, \phi)-$contractive mappings. Also, we give an application of our results as an integral equation.

The Sushila distribution is generalized in this article using the quadratic rank transmutation map as developed by Shaw and Buckley (2007). The newly developed distribution is called the Transmuted Sushila distribution (TSD). Various mathematical properties of the distribution are obtained. Real lifetime data is used to compare the performance of the new distribution with other related distributions. The results shown by the new distribution perform creditably well.

In regression modeling, first-order auto correlated errors are often a problem, when the data also suffers from independent variables. Generalized Least Squares (GLS) estimation is no longer the best alternative to Ordinary Least Squares (OLS). The Monte Carlo simulation illustrates that regression estimation using data transformed according to the GLS method provides estimates of the regression coefficients which are superior to OLS estimates. In GLS, we observe that in sample size $200$ and $\sigma$=3 with correlation level $0.90$ the bias of GLS $\beta_0$ is $-0.1737$, which is less than all bias estimates, and in sample size $200$ and $\sigma=1$ with correlation level $0.90$ the bias of GLS $\beta_0$ is $8.6802$, which is maximum in all levels. Similarly minimum and maximum bias values of OLS and GLS of $\beta_1$ are $-0.0816$, $-7.6101$ and $0.1371$, $0.1383$ respectively. The average values of parameters of the OLS and GLS estimation with different size of sample and correlation levels are estimated. It is found that for large samples both methods give similar results but for small sample size GLS is best fitted as compared to OLS.

In this paper, the interpolative Caristi type weakly compatible contractive in a complete metric space is applied to show some common fixed points results related to such mappings. Our application shows that the function which is used to prove the obtained results is a bounded map. An example is provided to show the useability of the acquired results.

This paper presents a two-step hybrid numerical scheme with one off-grid point for the numerical solution of general second-order initial value problems without reducing to two systems of the first order. The scheme is developed using the collocation and interpolation technique invoked on Bernstein polynomial. The proposed scheme is consistent, zero stable, and is of order four($4$). The developed scheme can estimate the approximate solutions at both steps and off-step points simultaneously using variable step size. Numerical results obtained in this paper show the efficiency of the proposed scheme over some existing methods of the same and higher orders.

This article deals with a nonlinear implicit fractional differential equation with nonlocal integral-multipoint boundary conditions in the frame of Hilfer fractional derivative. The existence and uniqueness results are obtained by using the fixed point theorems of Krasnoselskii and Banach. Further, to demonstrate the effectiveness of the main results, suitable examples are granted.

In this paper, we consider a class of boundary value problems for nonlinear two-term fractional differential equations with integral boundary conditions involving two $\psi $-Caputo fractional derivative. With the help of the properties Green function, the fixed point theorems of Schauder and Banach, and the method of upper and lower solutions, we derive the existence and uniqueness of positive solution of a proposed problem. Finally, an example is provided to illustrate the acquired results.

In this paper, we study the class of boundary value problems for a nonlinear implicit fractional differential equation with periodic conditions involving a ψ-Hilfer fractional derivative. With the help of properties Mittag-Leffler functions, and fixed-point techniques, we establish the existence and uniqueness results, whereas the generalized Gronwall inequality is applied to get the stability results. Also, an example is provided to illustrate the obtained results.

Motivated mainly by a variety of applications of Euler's Beta, hypergeometric, and confluent hypergeometric functions together with their extensions in a wide range of research fields such asengineering, chemical, and physical problems. In this paper, we introduce modified forms of some extended special functions such as Gamma function, Beta function, hypergeometric function and confluent hypergeometric function by making use of the idea given in reference \cite{9}. Also, certain investigations including summation formulas, integral representations and Mellin transform of these modified functions are derived. Further, many known results are obtained asspecial cases of our main results.

This paper discusses some existence results for at least one continuous solution for generalized fractional quadratic functional integral equations. Some results on nonlinear functional analysis including Schauder fixed point theorem are applied to establish the existence result for proposed equations. We improve and extend the literature by incorporated some well-known and commonly cited results as special cases in this topic. Further, we prove the existence of maximal and minimal solutions for these equations.

The given paper describes the implicit fractional differential equation with nonlinear integral boundary conditions in the frame of Caputo-Katugampola fractional derivative. We obtain an analogous integral equation of the given problem and prove the existence and uniqueness results of such a problem using the Banach and Krasnoselskii fixed point theorems. To show the effectiveness of the acquired results, convenient examples are presented.

Finsler geometry is a kind of differential geometry originated by P. Finsler. Indeed, Finsler geometry has several uses in a wide variety and it is playing an important role in differential geometry and applied mathematics of problems in physics relative, manual footprint. It is usually considered as a generalization of Riemannian geometry. In the present paper, we introduced some types of generalized $W^{h}$ -birecurrent Finsler space, generalized $W^{h}$ -birecurrent affinely connected space and we defined a Finsler space $F_{n}$ for Weyl's projective curvature tensor $W_{jkh}^{i}$ satisfies the generalized-birecurrence condition with respect to Cartan's connection parameters $\Gamma ^{\ast i}_{kh}$, such that given by the condition (\ref{2.1}), where $\left\vert m\right. \left\vert n\right. $ is\ h-covariant derivative of second order (Cartan's second kind covariant differential operator) with respect to $x^{m}$ \ and $x^{n}$ ,\ successively, $\lambda _{mn}$ and $\mu _{mn~}$ are\ non-null covariant vectors field and such space is called as a generalized $W^{h}$ -birecurrent\ space and denoted briefly by $GW^{h}$ - $BRF_{n}$ . We have obtained some theorems of generalized $W^{h}$ -birecurrent affinely connected space for the h-covariant derivative of the second order for Wely's projective torsion tensor $~W_{kh}^{i}$ , Wely's projective deviation tensor $~W_{h}^{i}$ in our space. We have obtained the necessary and sufficient condition forsome tensors in our space.

In this paper, we conclude that $n$-linear functionals spaces $\Im$ has approximate fixed points set, where $\Im$ is a non-empty bounded subset of an $n$-Banach space $H$ under the condition of equivalence, and we also use class of $(\mu,\sigma)$-nonexpansive mappings.