Rubayyi T. Alqahtani

Modelling the Spread of River Blindness Disease via the Caputo Fractional Derivative and the Beta-derivative

Information theory is used in many branches of science and technology. For instance, to inform a set of human beings living in a particular region about the fatality of a disease, one makes use of existing information and then converts it into a mathematical equation for prediction. In this work, a model of the well-known river blindness disease is created via the Caputo and beta derivatives. A partial study of stability analysis was presented. The extended system describing the spread of this disease was solved via two analytical techniques: the Laplace perturbation and the homotopy decomposition methods. Summaries of the iteration methods used were provided to derive special solutions to the extended systems. Employing some theoretical parameters, we present some numerical simulations.

Space-Time Spectral Collocation Algorithm for the Variable-Order Galilei Invariant Advection Diffusion Equations with a Nonlinear Source Term

This paper presents a space-time spectral collocation technique for solving the variable-order Galilei invariant advection diffusion equation with a nonlinear source term (VO-NGIADE). We develop a collocation scheme to approximate VONGIADE by means of the shifted Jacobi-Gauss-Lobatto collocation (SJ-GL-C) and shifted Jacobi-Gauss-Radau collocation (SJ-GR-C) methods. We successfully extend the proposed technique to solve the two-dimensional space VO-NGIADE. The discussed numerical tests illustrate the capability and high accuracy of the proposed methodologies.

Mathematical analysis of bioethanol production through continuous reactor with a settling unit

Abstract Bioethanol generated from biomass and bioenergy crops has been promulgated as one of the most feasible alternatives to fossil fuel, as it is considered to be clean, green and of course renewable. In this paper, we develop a nonlinear chemostat model for bioethanol production. The growth rate is given by a modified Andrew expression with inhibition by ethanol, which is often used to model the growth of biomass. Then the uniqueness, invariance and dissipation of solutions of the model are established. Steady state solutions of the model and their stability are also determined as a function of the residence time. We also investigate the effects of the model parameters on a physically valid region. Finally, we compare the performance of a reactor, using a recycling process, against that of without recycling process. With a substrate feed concentration of 100 g/L, there is a critical value of the residence time which identifies a turning point in the reactor performance for the removal of substrate.