In this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynamics of our proposed model.
This study was done to investigate the antibacterial effect of the three types of Lawsonia inermis linn (henna) leaf extracts (water, methanol and chloroform) in different concentrations (40, 80, 120) mg/ml against four strains of bacteria (Staphyllococus aureus, Bacillus subtilis, Pseudomonos aerogenosa and Eschorichia coli) in vitro using ager well diffusion method. Water extract showed the highest antibacterial activity, followed by methanol extract, while the chloroform extract showed the lowest activity. The maximum inhibition zone of water extract was observed against , Pseudomonos aerogenosa (25mm) in the concentration (120) mg/ml, while the minimum zone of inhibition (9mm) was in Bacillus subtilis in the same concent
... Show MoreIn this study, a total of 209 individuals of leeches were collected from Al-Hindyia River / Babil Province. 116 individuals were identified as Erpobdella octaculata (Linnaeus, 1758), 50 individuals as Erpobdella punctata (Leidy,1870) and 43 individuals as Hemiclepsis marginata (Müller, 1774). Four samples were collected monthly during a period from February to June 2018. Some physical and chemical water properties were also examined, including air and water temperature, potential of hydrogen pH, Electrical Conductivity EC, Total Dissolved Solid TDS, Dissolved Oxygen DO, and the Biological Oxygen Demand BOD₅. Air and water temperature were r
... Show MoreIn this study, an efficient novel technique is presented to obtain a more accurate analytical solution to nonlinear pantograph differential equations. This technique combines the Adomian decomposition method (ADM) with the homotopy analysis method concepts (HAM). The whole integral part of HAM is used instead of an integral part of ADM approach to get higher accurate results. The main advantage of this technique is that it gives a large and more extended convergent region of iterative approximate solutions for long time intervals that rapidly converge to the exact solution. Another advantage is capable of providing a continuous representation of the approximate solutions, which gives better information over whole time interv
... Show MoreA dynamic analysis method has been developed to investigate and characterize embedded delamination on the dynamic response of composite laminated structures. A nonlinear finite element model for geometrically large amplitude free vibration intact plate and delamination plate analysis is presented using higher order shear deformation theory where the nonlinearity was introduced in the Green-Lagrange sense. The governing equation of the vibrated plate were derived using the Variational approach. The effect of different orthotropicity ratio, boundary condition and delamination size on the non-dimenational fundamental frequency and frequency ratios of plate for different stacking sequences are studied. Finally th
... Show MoreWe extended the characterization of strict local minimizers of order two in ward,s
theorem for nonlinear problem to a certain class of nonsmooth semi-infinite problems with inequality constraints in the nonparametric constraint case.
In this paper, we study the growth of solutions of the second order linear complex differential equations insuring that any nontrivial solutions are of infinite order. It is assumed that the coefficients satisfy the extremal condition for Yang’s inequality and the extremal condition for Denjoy’s conjecture. The other condition is that one of the coefficients itself is a solution of the differential equation .
A perturbed linear system with property of strong observability ensures that there is a sliding mode observer to estimate the unknown form inputs together with states estimation. In the case of the electro-hydraulic system with piston position measured output, the above property is not met. In this paper, the output and its derivatives estimation were used to build a dynamic structure that satisfy the condition of strongly observable. A high order sliding mode observer (HOSMO) was used to estimate both the resulting unknown perturbation term and the output derivatives. Thereafter with one signal from the whole system (piton position), the piston position make tracking to desire one with a simple linear output feedback controller after ca
... Show MoreThis paper is concerned with combining two different transforms to present a new joint transform FHET and its inverse transform IFHET. Also, the most important property of FHET was concluded and proved, which is called the finite Hankel – Elzaki transforms of the Bessel differential operator property, this property was discussed for two different boundary conditions, Dirichlet and Robin. Where the importance of this property is shown by solving axisymmetric partial differential equations and transitioning to an algebraic equation directly. Also, the joint Finite Hankel-Elzaki transform method was applied in solving a mathematical-physical problem, which is the Hotdog Problem. A steady state which does not depend on time was discussed f
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