The major aim of this work is to apply a technique, Elzaki transform (ET), which is an iterative analytical technique to achieve an approximate analytical solution for some applications of nonlinear differential equations. This technique depends on applying ET which has been used to break down the partial differential equation solution into an infinite number of components. Moreover, some illustrative examples are given and the results obtained indicate the proposed method’s accuracy, efficiency, and reliability. Results like this demonstrate how effective and efficient this method is in resolving problems of this kind. Therefore, using fractional differential equations as a model, our suggested approach can be used to analyze the solutions of a broad range of genuine issues that arise in the natural sciences and engineering.
This paper presents a comparative study of two learning algorithms for the nonlinear PID neural trajectory tracking controller for mobile robot in order to follow a pre-defined path. As simple and fast tuning technique, genetic and particle swarm optimization algorithms are used to tune the nonlinear PID neural controller's parameters to find the best velocities control actions of the right wheel and left wheel for the real mobile robot. Polywog wavelet activation function is used in the structure of the nonlinear PID neural controller. Simulation results (Matlab) and experimental work (LabVIEW) show that the proposed nonlinear PID controller with PSO
learning algorithm is more effective and robust than genetic learning algorithm; thi
Background: This in vitro study was carried out to investigate the effect of post space regions (coronal, middle and apical), the effect of post types ( Manually Milled Zirconia post, Prefabricated Fiber post, prefabricated Zirconia post) and the type of cement used (GIC, self-adhesive resin cement) on the bond strength between the posts and root dentin by using push-out test. Material and methods: Forty eight mandibular premolars extracted for orthodontic reasons (single rooted) were instrumented with ProTaper system (hand use) and obturated with gutta percha for ProTaper using AH26® root canal sealer following the manufacturer instructions. After 24 hours, post space was prepared using Zirix and Glassix drills no.3 creating 8 mm dept
... Show MoreThis research is a study of the difficulties of learning the Arabic language that faces Arabic language learners in the Kurdistan Region, by revealing its types and forms, which can be classified into two categories:
The first type has difficulties related to the educational system, the source of which is the Arabic language itself, the Arabic teacher or the learner studying the Arabic language or the educational curriculum, i.e. educational materials, or the educational process, i.e. the method used in teaching.
The second type: general difficulties related to the political aspect, the source of which is the policy of the Kurdistan Regional Government in marginalizing the Arabic language and replacing the forefront of th
... Show MoreThe non static chain is always the problem of static analysis so that explained some of theoretical work, the properties of statistical regression analysis to lose when using strings in statistic and gives the slope of an imaginary relation under consideration. chain is not static can become static by adding variable time to the multivariate analysis the factors to remove the general trend as well as variable placebo seasons to remove the effect of seasonal .convert the data to form exponential or logarithmic , in addition to using the difference repeated d is said in this case it integrated class d. Where the research contained in the theoretical side in parts in the first part the research methodology ha
... Show MoreA new panel method had been developed to account for unsteady nonlinear subsonic flow. Two boundary conditions were used to solve the potential flow about complex configurations of airplanes. Dirichlet boundary condition and Neumann formulation are frequently applied to the configurations that have thick and thin surfaces respectively. Mixed boundary conditions were used in the present work to simulate the connection between thick fuselage and thin wing surfaces. The matrix of linear equations was solved every time step in a marching technique with Kelvin's theorem for the unsteady wake modeling. To make the method closer to the experimental data, a Nonlinear stripe theory which is based on a two-dimensional viscous-inviscid interac
... Show MoreIn this paper, the general framework for calculating the stability of equilibria, Hopf bifurcation of a delayed prey-predator system with an SI type of disease in the prey population, is investigated. The impact of the incubation period delay on disease transmission utilizing a nonlinear incidence rate was taken into account. For the purpose of explaining the predation process, a modified Holling type II functional response was used. First, the existence, uniform boundedness, and positivity of the solutions of the considered model system, along with the behavior of equilibria and the existence of Hopf bifurcation, are studied. The critical values of the delay parameter for which stability switches and the nature of the Hopf bifurcat
... Show MoreIn this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R3 is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.
Mathematical Subject Classificat
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