This paper presents the implementation of a complex fractional order proportional integral derivative (CPID) and a real fractional order PID (RPID) controllers. The analysis and design of both controllers were carried out in a previous work done by the author, where the design specifications were classified into easy (case 1) and hard (case 2) design specifications. The main contribution of this paper is combining CRONE approximation and linear phase CRONE approximation to implement the CPID controller. The designed controllers-RPID and CPID-are implemented to control flowing water with low pressure circuit, which is a first order plus dead time system. Simulation results demonstrate that while the implemented RPID controller fails to stabi

In this paper,  a Sokol-Howell prey-predator model involving strong Allee effect is proposed and analyzed. The existence, uniqueness, and boundedness are studied. All the five possible equilibria have been are obtained and their local stability conditions are established. Using Sotomayor's theorem, the conditions of local saddle-node and transcritical and pitchfork bifurcation are derived and drawn. Numerical simulations are performed to clarify the analytical results

In most of Beckett’s plays , there are prominent elements of absurdity that are landmarks of his style and the way of his writing like : the physical and the spiritual decay of characters, the disintegration of language as it becomes no longer a means of human communication because there is an inability to establish any kind of mental contact among them. These elements are quite apparent in Beckett’s “All That Fall”. The play exhibits a list of  conflicts: one is between powerful forces as that between the force of life represented by Maddy and the forces of death represented by Dan .The second is  the conflict and contempt between the old generation and the new one in the case of Dan’s desire to kill the boy fetching

This paper presents a novel idea as it investigates the rescue effect of the prey with fluctuation effect for the first time to propose a modified predator-prey model that forms a non-autonomous model. However, the approximation method is utilized to convert the non-autonomous model to an autonomous one by simplifying the mathematical analysis and following the dynamical behaviors. Some theoretical properties of the proposed autonomous model like the boundedness, stability, and Kolmogorov conditions are studied. This paper's analytical results demonstrate that the dynamic behaviors are globally stable and that the rescue effect improves the likelihood of coexistence compared to when there is no rescue impact. Furthermore, numerical simul

This paper presents an analytical study for the magnetohydrodynamic (MHD) flow of a generalized Burgers’ fluid in an annular pipe. Closed from solutions for velocity is obtained by using finite Hankel transform and discrete Laplace transform of the sequential fractional derivatives. Finally, the figures are plotted to show the effects of different parameters on the velocity profile.

Coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has become a pandemic worldwide. On a daily basis the number of deaths associated with COVID-19 is rapidly increasing. The main transmission route of SARS-CoV-2 is through the air (airborne transmission). This review details the airborne transmission of SARS-CoV-2, the aerodynamics, and different modes of transmission (e.g. droplets, droplet nuclei, and aerosol particles). SARS-CoV-2 can be transmitted by an infected person during activities such as expiration, coughing, sneezing, and talking. During such activities and some medical procedures, aerosols and droplets contaminated with SARS-CoV-2 particles are formed. Depending on their