Open Access Method Article

Combined Optimized SFGM(1,1,k) Model and Its Application in Total Import and Export

Lang Yu, Xiwang Xiang

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/jamcs/2019/v31i330111

Since the introduction of the fractional FGM(1,1) model, it has been widely used in all aspects of society. However, the original FGM(1,1) model has certain defects. Therefore, many experts and scholars have proposed many optimization methods for the shortcomings of the fractional FGM(1,1) model, and have been well applied. Since the gray action of the FGM(1,1) model is a fixed constant, the dynamic variation characteristics of the system cannot be well described. Based on this, this paper proposes a new SFGM(1,1,k) model by optimizing the gray action amount and reconstructing the background value of the optimized model using Simpson formula to improve the FGM(1,1) model. Then, apply it to the numerical examples of import and export totals. The results show that the combined optimization of SFGM(1,1,k) has higher fitting accuracy and better prediction effect. The validity and practicability of the SFGM(1,1,k) model are verified. The application range of FGM(1,1) model is extended.

Open Access Original Research Article

Gaussian Generalized Tetranacci Numbers

Yüksel Soykan

Journal of Advances in Mathematics and Computer Science, Page 1-21
DOI: 10.9734/jamcs/2019/v31i330112

In this paper, we dene Gaussian generalized Tetranacci numbers and as special cases, we investigate Gaussian Tetranacci and Gaussian Tetranacci-Lucas numbers with their properties. We present Binet's formulas, generating functions, and the summation formulas for Gaussian generalized Tetranacci numbers.Moreover, we give some identities connecting Gaussian Tetranacci and Gaussian Tetranacci-Lucas numbers. Furthermore, we present matrix formulation of Gaussian generalized Tetranacci numbers.

Open Access Original Research Article

Stochastic Optimal Control Model of Haemorrhagic Conjunctivitis Disease

Sacrifice Nana-Kyere, Desmond Titus Banon, Seth N. Marmah, Daniel Kwarteng

Journal of Advances in Mathematics and Computer Science, Page 1-19
DOI: 10.9734/jamcs/2019/v31i330113

In this research article, a model for the transmission dynamics of haemorrhagic conjunctivitis disease is presented. The tool of dynamical system is employed in investigating the potency of the spreading of the epidemic. The analysis revealed the likelihood of the epidemic to spread when the basic reproduction number exceeds one. The model is reformulated as optimal control problem to assess the effectiveness of the proposed control strategy. Maximum Principle was employed to derive the necessary conditions for the existence of optimal control. Numerical solution of the optimality was derived and computed to investigate the optimum control strategy that would be efficacious to be implemented in reducing the number of exposed and infected individuals. Stochastic version of the model is deduced by introducing stochastic perturbations in the deterministic one. Numerical simulations are provided to illustrate the differences in the dynamics of the models and to understand the epidemic phenomenon.

Open Access Original Research Article

Open Access Original Research Article

MHD Maxwell Reactive Flow with Velocity Slip Over a Stretching Surface with Prescribed Heat Flux in the Presence of Thermal Radiation in a Porous Medium

I. G. Baoku, K. I. Falade

Journal of Advances in Mathematics and Computer Science, Page 1-25
DOI: 10.9734/jamcs/2019/v31i330116

This article is concerned with the study of heat and mass transfer of a MHD reactive flow of an upper-convected Maxwell fluid model over a stretching surface subjected to a prescribed heat flux with velocity slip effect in a Darcian porous medium in the presence of thermal radiation and internal heat generation/absorption. The basic boundary layer governing partial differential equations are transformed into a set of coupled ordinary differential equations, which are solved numerically using Runge-Kutta-Fehlberg integration scheme with shooting technique. The far field boundary conditions are asymptotically satisfied to support the accuracy of the numerical computations and the results obtained. The velocity, temperature and species concentration profiles are enhanced by increasing values of velocity slip parameter with Hartmann number, heat generation/absorption parameter and order of chemical reaction parameter respectively.  Increments in the values of velocity slip parameter, Hartmann number, rate of chemical reaction parameter and Prandtl number boost the wall shear stress, dimensionless surface temperature is increased by increasing values of Deborah number, heat generation/absorption and order of chemical reaction parameters while local rate of mass transfer is enhanced by increments in the values of Hartmann number, suction velocity, Darcian porous medium, rate of chemical reaction and velocity slip parameters. The presence of velocity slip on the flow distribution is found to be of great significance to the study.