In this paper, by using the Ge and Ren extension of coincidence degree theory, we established the existence of a solution for a resonant mixed fractional order p-Laplacian boundary value problem (BVP) on the half-line. In the process, we solved the corresponding homogeneous fractional order BVP for conditions critical for resonance and showed that the operator A(x,λ)(t) constructed from the abstract equation Mx(t)=Nx(t) is relatively compact. The results are demonstrated with an example.

In this work, we use the Ge and Ren extension of Mawhin's coincidence degree theory to investigate the solvability of the p-Laplacian fractional order boundary value problem of the form (phi(p)(D(0+)(alpha)x(t)))' = f(t, x(t), D(0+)(alpha-3)x(t), D(0+)(alpha-2)x(t), D(0+)(alpha)(-1)x(t), D(0+)(alpha)x(t)), t is an element of (0, + infinity) x(0) = 0 = D(0+)(alpha-3)x(0), D(0+)(alpha-2)x(0) = integral(1 )(0)D(0+)(alpha-2)x(t)dA(t), lim(t ->+infinity) D(0+)(alpha)(-1)x(t) = Sigma(m)(i=1) (sic)(i)D(0+)(alpha)(-1)x(xi(i)), D(0+)(alpha)(-1)x(infinity) = 0, where 3 < alpha <= 4. The conditions integral(1)(0) dA(t) = 1, integral(1)(0) tdA(t) = 0, Sigma(m)(i=1) (sic)(i )and Sigma(m)(i=1) (sic)(i)xi(-1)(i) = 0 are critical for resonance.

This paper derives existence results for a resonant fractional order differential equation with two-dimensional kernel on the half-line using coincidence degree theory.Fractional calculus of Riemann-Liouville type is adopted in the study.The results obtained are illustrated with an example.

This paper studied delay differential equation (DDE) model in mathematical biology and investigated stability analysis of the dynamical behaviour of susceptible, infectious and recovered (SIR) disease epidemic model with finite discrete delay. Using the reproduction number , as the threshold theorem of epidemiology for disease free equilibrium (DFE), the paper applies the more general Hopf bifurcation theorem using the methods of normal form concept and Center Manifold Theorem (CMT) to investigate the stability of the delay model where linearisation method does not apply. The result of the behavior of the model obtained showed that the conditions of the more general bifurcation theorem from the dynamical system is sufficient but not necessary as the model is unable to stabilise the unstable interior non-hyperbolic equilibrium due to Hopf bifurcation. Specifically, the direction of the Hopf bifurcation, the stability and the period of the bifurcating periodic solutions of the non-hyperbolic disease reduced epidemic model were explicitly determined by applying the CMT to the perturbed operator differential equation (OpDE) where the linearised equation has at least one characteristic root with zero real part while every other eigenvalue has negative real parts. Finally, numerical simulations to verify the analytical findings in support of stability for the disease epidemic model were performed using MATLAB software. To ensure model relevance, the study is recommended to ecologists, biologists and public health workers.

this paper investigates existence of solutions of a resonant fractional order boundary value problem with mul-tipoint and Riemann-Stieltjes integral boundary conditions on the half-line with two-dimensional kernel. We utilised Mawhin's coincidence degree theory to derive our results. The results obtained are validated with examples.

This paper presents the development and implementation of a numerical method forthe solution of one dimensional Mixed Fredholm Volterra Intergro-Differential Equations(MFVIDEs). The new technique transformed MFVIDEs into an integral equation whichis then approximated using a polynomial collocation method. Standard collocation pointsare then used to convert the problem into a system of algebraic equations. Some numericalexamples are used to test the efficiency and accuracy of the method. The results showthat the new method is efficient, accurate and easy to implement.

Screened plant species with potential for green belt development can act as eco-sustainable tools for restoring the polluted ecosystem. Eight plant species from two study locations in Ado-Odo, Ota, Ogun State, Nigeria, were examined to identify their air pollution response and performance by deploying two air pollution indices, namely air pollution tolerance index (APTI) and anticipated performance index (API). APTI results identified all screened plants as sensitive species suitable as bio-indicators of air pollution, with Ficus auriculata (2.42) common to the non-industrial location being the most sensitive. API scores categorized Ficus auriculata (56.25%) as a moderate performer, while Syzygium malaccense (75%) and Mangifera indica (75%) were identified as very good performers, suitable for green belt development. The relationship between each biochemical parameter with APTI was investigated using regression analysis and two-way analysis of variance. The model result showed a significant relationship between each biochemical parameter with APTI, and relative water content had the highest influence on APTI (R-2 = 0.99436). Both indices (APTI and API) are suitable for screening and recommending native plant species for cultivation in the polluted environment, thus promoting ecological restoration. Hence, Syzygium malaccense, Mangifera indica and Ficus auriculata, respectively, were recommended for green belts design. Further intensive screening to identify tolerant species and best to excellent performer's trees suitable for restoring the ecosystem is advised.

The study investigates stability analysis of Nicholson-blowflies’ equation with a linear harvesting function, where sufficient conditions are obtained for nontrivial equilibrium of a delayed model using the corresponding characteristic equation and Hopf bifurcation analysis. The Hopf bifurcation is studied for the qualitative character of the dynamical system, and conditions for the existence of periodic oscillation are identified. The periodic orbit of the model is equally investigated, from which further chaotic results are obtained using numerical example via MATLAB software. The study supplements theoretical improvement to earlier results obtained in the literature.

UK-based Hindawi (now part of Wiley) is one of the larger open access (OA) publishers that levies article processing charges (APCs) for publication in its 220 OA journals. The APCs range between US$650 and US$2300, with a median of US$950. We assessed if there is a link between the APC of Hindawi journals and two metrics, Elsevier’s Scopus CiteScore, and Clarivate’s Journal Impact Factor (JIF). Whereas 163 journals have a CiteScore (median APC = US$1000), 71 have a JIF (median APC = US$1950), while others with neither a CiteScore nor a JIF (NCNJ) have a median APC of US$650. The APC of journals with a CiteScore differed significantly from those with a JIF. We found a significant positive correlation between CiteScore and AFPC (r = 0.223, p < 0.01), but a weak non-significant positive correlation between JIF and APC (r = 0.162, p = 0.177). The Kruskal Wallis test showed that the medians of three groups (CiteScore, JIT and NCNJ) differed significantly from each other at p < 0.05.

The paper investigates the stability of the SIR mathematical model of transmission of an infectious disease with delay. First, the study investigates local stability of the positive steady state of an infectious disease model by analyzing the linearised system where more general stability criteria with delay and model parameters are obtained. Secondly, the study shows that the model exhibits Hopf bifurcation on choosing the delay as a bifurcation parameter. Conditions for existence of qualitative behaviour for positive steady state are identified. Finally, numerical simulation of results and biological interpretations were verified using MATLAB software for the delay model. The study supplements theoretical improvement to earlier results obtained in the literature.

This present paper considers the approximate-analytical solution of some classical Riccati Differential Equations (RDEs). Here, an efficient numerical method referred to as Daftardar-Gejji Jafari Method (DJM) for solving the functional differential equations is applied. Three numerical examples are considered to show the accuracy of the proposed method.

We propose a near exact equation that links the quantile function and its quartiles of beta distribution (BD). This is done with the use of quantile mechanics approach whereby the probability density function of beta distribution is transformed into second order nonlinear ordinary differential equations whose solutions give the required inverse cumulative distribution function of the distribution. The median can easily be obtained from the proposed equations. Further efforts are required to refine and simplify the results. The results from this paper will greatly affect the way, beta distribution is used in engineering, in general, and wireless communications, in particular. Furthermore, the results obtained are very close the machine values.

Hepatitis B is caused by the hepatitis B virus (HBV) and it affects livers. It has been established that the disease is a serious medical condition caused by an overpowering immune response to infection. To this effect, there is a need for cross examination of records of patients on this disease to ascertain the factors that could be responsible for the survival or dying from this disease. Descriptive analysis of the data showed that sexually active age bracket (31 – 50) are greatly affected by the disease while female accounted for majority of those that are tested positive to the disease. Chi squared statistic was used to test for independence between age and gender of those who tested positive to disease between 2006 and 2015 in Lagos state, Nigeria. It was discovered that, both variables of age and gender are not independent which means there is association between the Age and Gender of HBV patients.

The Multidisciplinary Digital Publishing Institute (MDPI) is a prominent open access (OA) publisher that uses article processing charges (APCs) as its business model. Our objective was to determine the association between the APCs levied by MDPI journals and 1) their inclusion in Scopus and Web of Science databases or 2) their stature, as represented by their CiteScore (Elsevier’s Scopus) and Impact Factor (awarded by Clarivate Analytics). Among the 227 journals published by MDPI, 51 had both IF and CiteScore; 107, only a CiteScore; and 84, neither IF nor CiteScore. The charges levied by the journals varied widely, from 0 to CHF 2000 (Swiss francs), the most frequent figure (159 journals) being CHF 1000, or about €930. The amount of APCs was found to be correlated to IF (R² = 0.64; p <0.001; 107 journals) and also to CiteScore (R² = 0.619; p <0.001; 53 journals). The charges levied by journals that had both IF and CiteScore were significantly higher than those charged by journals with neither IF nor CiteScore (p <0.05). The charges were also correlated to the age of the journal: the more recently launched journals charged less than the older journals did.

Quantile function or inverse cumulative distribution function (CDF) is heavily utilized in modelling, simulation, reliability analysis and random number generation. The use is often limited if the inversion method fails to estimate it from the cumulative distribution function. As a result, approximation becomes the other feasible option. The failure of the inversion method is often due to the intractable nature of the CDF of the distribution. Approximation may come in the form of series expansions, closed form or functional approximation, numerical algorithm and the closed form expression drafted in terms of the quantile function of another distribution. This work used the cubic spline interpolation to obtain the closed form of the inverse cumulative distribution function of the Nakagami-m distribution. Consequently, the closed form of the quantile function obtained for the selected parameters of the distribution serves as an approximation which compares favourably with the R software values. The result obtained was a significant improvement over some results surveyed from literature for four reasons. Firstly, the approximates produced better results in simulation as evidenced by the some values of the root mean square error of this work when compared with others. Secondly, the result obtained at the extreme tail of the distribution is better than others selected from the literature. Thirdly, the closed form estimates are easy to compute and save computation time. The closed form of the quantile function obtained in this work can be used in simulating Nakagami random variables which are used in modelling attenuation and fading channels in wireless communications and ultrasonic tissue characterization.

Chi square distribution is a continuous probability distribution primarily used in hypothesis testing, contingency analysis, and construction of confidence limits in inferential statistics but not necessarily in the modeling of real-life phenomena. The closed-form expression for the quantile function (QF) of Chi square is not available because the cumulative distribution function cannot be transformed to yield the QF and consequently places limitations on the use of the QF. Researchers have over the years proposed approximations that improve over time in terms of speed, computational efficiency, and precision, and so on. However, most of the available closed-form expressions (quantile approximation) fail at the extreme tails of the distribution. This paper used the Quantile mechanics approach to obtain second-order nonlinear ordinary differential equations whose solutions using the power series method yielded initial approximates in form of series for different values of the degrees of freedom. The initial approximate varies with the exact (R software) values which serve as the reference and the error between them was minimized by the natural cubic spline interpolation. The final approximates are correct up to an average of 8 decimal places, have small error, and is closer to the exact when compared with some other results from other researchers. The upper tail of the distribution was considered and excellent results were obtained which is a major improvement over the existing results in the literature. The approach used in this work is a hybrid of series expansions and numerical algorithms. Computer codes can be written for the application.

The use of quantile functions of probability distributions whose cumulative distribution is intractable is often limited in Monte Carlo simulation, modeling, and random number generation. Gamma distribution is one of such distributions, and that has placed limitations on the use of gamma distribution in modeling fading channels and systems described by the gamma distribution. This is due to the inability to find a suitable closed-form expression for the inverse cumulative distribution function, commonly known as the quantile function (QF). This paper adopted the Quantile mechanics approach to transform the probability density function of the gamma distribution to second-order nonlinear ordinary differential equations (ODEs) whose solution leads to quantile approximation. Closed-form expressions, although complex of the QF, were obtained from the solution of the ODEs for degrees of freedom from one to five. The cases where the degree of freedom is not an integer were obtained, which yielded values closed to the R software values via Monte Carlo simulation. This paper provides an alternative for simulating gamma random variables when the degree of freedom is not an integer. The results obtained are fast, computationally efficient and compare favorably with the machine (R software) values using absolute error and Kullback–Leibler divergence as performance metrics.

In this paper, the solution of Klein Gordon Equation is sought. Frobenius method was used to solve the Klein Gordon (KG) equation with equal scalar and vector harmonic oscillator plus inverse quadratic potential for s - waves. A corresponding un-normalized wavefunction was obtained for the Frobenius equation in the form of a power series.