International Journal of Mathematics and Mathematical Sciences

A boundary value problem for a nonhomogeneous heat equation with a load in the form of a fractional Riemann–Liouville integral of an order is considered. By inverting the differential part, the problem is reduced to an integral equation with a kernel with a special function. The special function is presented as a generalized hypergeometric function. The limiting cases of the order of the fractional derivative are studied: it is shown that the interval for changing the order of the fractional derivative can be expanded to integer values . The results of the study remain unchanged. The kernel of the integral equation is estimated. Conditions for the solvability of the integral equation are obtained.

In this paper, the impact of viral illnesses on the predator-prey relationship with an optimal control analysis is studied. An ecoepidemiological model of four compartments, namely, susceptible prey, susceptible predator, infected prey, and infected predator populations, in the interaction of the prey-predator system is formulated. The fundamental tenet of our ecoepidemiology model is that sick predators do not engage in predation. It is confirmed that the system’s solution exists, is positive, and is bounded. The system’s equilibrium points are determined and computed. Lyapunov functions and a linearizing form are used for local and global stability analysis, respectively. The next generation matrix approach is used to calculate the threshold value for diseased predators and prey at the disease-free equilibrium point. Optimal treatment options for vulnerable and infected populations are established by applying optimal control theory to the ecoepidemiology model of a prey-predator system. MATLAB software is utilized to obtain numerical simulations that validate the analytical outcomes. The optimal control problem simulations demonstrate that the number of infected populations in a given prey-predator system can be decreased by implementing control measures.

In literature, several types of join operations of two graphs based on subdivision graph, -graph, -graph, and total graph have been introduced, and their spectral properties have been studied. In this paper, we introduce a new double join operation based on -merged subdivision graph. We compute the spectrum of a special block matrix and then use it to describe the distance spectra of some double join operations of graphs. At last, we give several families of distance equienergetic graphs of diameter 3.

This work is an attempt to apply Lambert series in the theory of univalent functions. We first consider the Hadamard product of Rabotnov function and Lambert series with coefficients derived from the arithmetic function to introduce a normalized linear operator . We then acquire sufficient conditions for to be univalent, starlike and convex, respectively. Furthermore, we discuss the inclusion results in some special classes, namely, spiral-like and convex spiral-like subclasses. In addition, we extend the findings by incorporating two Robin’s inequalities, one of which is analogous to the Riemann hypothesis.

For non-negative integers and , if and are two partitions of a graph ’s vertex set , such that and induce two subgraphs of , called with maximum degree at most and with maximum degree at most , respectively, then the graph is said to be improper -colorable, as well as -colorable. A class of planar graphs without , and is denoted by . In 2019, Dross and Ochem proved that is -colorable, for each graph in . Given that , this inspires us to investigate whether is -colorable, for each graph in . In this paper, we provide a partial solution by showing that is (3, 3)-colorable, for each graph in .

Understanding the factors that influence COVID-19 transmission is essential in assessing and mitigating the spread of the pandemic. This study focuses on modeling the impact of air pollution and meteorological parameters on the risk of COVID-19 transmission in Western Cape Province, South Africa. The data used in this study consist of air pollution parameters, meteorological variables, and COVID-19 incidence observed for 262 days from April 26, 2020, to January 12, 2021. Lagged data were prepared for modeling based on a 6-day incubation period for COVID-19 disease. Based on the overdispersion property of the incidence, negative binomial (NB) and generalised Poisson (GP) regression models were fitted. Stepwise regression was used to select the significant predictors in both models based on the Akaike information criterion (AIC). The residuals of both NB and GB regression models were autocorrelated. An autoregressive integrated moving average (ARIMA) model was fitted to the residuals of both models. ARIMA (7, 1, 5) was fitted to the residuals of the NB model while ARIMA (1, 1, 6) was fitted for the residuals of the GP model. NB + ARIMA (7, 1, 5) and GP + ARIMA (1, 1, 6) models were tested for performance using root mean square error (RSME). GP + ARIMA (1, 1, 6) was selected as the optimal model. The results from the optimal model suggest that minimum temperature, ambient relative humidity, ambient wind speed, , and at various lags are positively associated with COVID-19 incidence while maximum relative humidity, minimum relative humidity, solar radiation, maximum temperature, NO, PM load, , , and at various lags have a negative association with COVID-19 incidence. Ambient wind direction and temperature showed a nonsignificant association with COVID-19 at all lags. This study suggests that meteorological and pollution parameters play a vital independent role in the transmission of the SARS-CoV-2 virus.