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Optimal Control Design of the In-vivo HIV Fractional Model

    HIV is a leading cause of death, in particular, in Sub-Saharan Africa. In this paper, a fractional differential system in vivo deterministic models for HIV dynamics is presented and analyzed. The main roles played by different HIV treatment methods are investigated using fractional optimal control theory. We use three treatment regimens as system control variables to determine the best strategies for controlling the infection. The optimality system is numerically solved using the fractional Adams-Bashforth technique.

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Publication Date
Tue Jan 02 2007
Journal Name
Journal Of The Faculty Of Medicine Baghdad
CMV infection among HIV / AIDS patients in Iraq

Background: The aim of the study was to determine the prevalence of CMV infection among HIV / AIDS patients in relation to disease progression, and to study the mortality during the period of the study.
Patients and Methods: The study included 155 HIV/AIDS patients (148 HIV- infected and seven AIDS patients) and 122 apparently "healthy" controls. CMV (IgG and 1gM) antibodies were determined by ELISA. The patients were followed up for a period of nine months, and retested frequently for development of active CMV infection.
Results: The prevalence of CMV (IgG) antibodies in the HIV/AIDS patients was 100%. A significant higher prevalence of CMV (IgM) among AIDS patients (42.9°/6) than among HIV infected

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Publication Date
Sat Jun 27 2020
Journal Name
Iraqi Journal Of Science
On Analytical Solution of Time-Fractional Type Model of the Fisher’s Equation

In this paper, the time-fractional Fisher’s equation (TFFE) is considered to exam the analytical solution using the Laplace q-Homotopy analysis method (Lq-HAM)”. The Lq-HAM is a combined form of q-homotopy analysis method (q-HAM) and Laplace transform. The aim of utilizing the Laplace transform is to outdo the shortage that is mainly caused by unfulfilled conditions in the other analytical methods. The results show that the analytical solution converges very rapidly to the exact solution.

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Publication Date
Tue Oct 30 2018
Journal Name
Journal Of Engineering
Active Vibration Control of Cantilever Beam by Using Optimal LQR Controller

Many of mechanical systems are exposed to undesired vibrations, so designing an active vibration control (AVC) system is important in engineering decisions to reduce this vibration. Smart structure technology is used for vibration reduction. Therefore, the cantilever beam is embedded by a piezoelectric (PZT) as an actuator. The optimal LQR controller is designed that reduce the vibration of the smart beam by using a PZT element.  

In this study the main part is to change the length of the aluminum cantilever beam, so keep the control gains, the excitation, the actuation voltage, and mechanical properties of the aluminum beam for each length of the smart cantilever beam and observe the behavior and effec

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Publication Date
Tue Dec 01 2020
Journal Name
Baghdad Science Journal
Existence And Controllability Results For Fractional Control Systems In Reflexive Banach Spaces Using Fixed Point Theorem

       In this paper, a fixed point theorem of nonexpansive mapping is established to study the existence and sufficient conditions for the controllability of nonlinear fractional control systems in reflexive Banach spaces. The result so obtained have been modified and developed in arbitrary space having Opial’s condition by using fixed point theorem deals with nonexpansive mapping defined on a set has normal structure. An application is provided to show the effectiveness of the obtained result.

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Publication Date
Wed Jan 20 2021
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Necessary Condition for Optimal Boundary Control Problems for Triple Elliptic Partial Differential Equations

       In this work, we prove that the triple linear partial differential equations (PDEs) of elliptic type (TLEPDEs) with a given classical continuous boundary control vector (CCBCVr) has a unique "state" solution vector (SSV)  by utilizing the Galerkin's method (GME). Also, we prove the existence of a classical continuous boundary optimal control vector (CCBOCVr) ruled by the TLEPDEs. We study the existence solution for the triple adjoint equations (TAJEs) related with the triple state equations (TSEs). The Fréchet derivative (FDe) for the objective function is derived. At the end we prove the necessary "conditions" theorem (NCTh) for optimality for the problem.

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Publication Date
Fri Sep 30 2022
Journal Name
Iraqi Journal Of Science
Existence, Uniqueness and Approximate Controllability of Impulsive Fractional Nonlinear Control System with Nonsingular Kernel

     The main aim of this work is to investigate the existence and approximate controllability of mild solutions of impulsive fractional nonlinear control system with a nonsingular kernel in infinite dimensional space. Firstly, we set sufficient conditions to demonstrate the existence and uniqueness of the mild solution of the control system using the Banach fixed point theorem. Further, we prove the approximate controllability of the control system using the sequence method.

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Publication Date
Fri Jan 26 2024
Journal Name
Iraqi Journal Of Science
Effect of Mhd on Accelerated Flows of A Viscoelastic Fluid with The Fractional Burgers’ Model

In this paper, we studied the effect of magnetic hydrodynamic (MHD) on accelerated flows of a viscoelastic fluid with the fractional Burgers’ model. The velocity field of the flow is described by a fractional partial differential equation of fractional order by using Fourier sine transform and Laplace transform, an exact solutions for the velocity distribution are obtained for the following two problems: flow induced by constantly accelerating plate, and flow induced by variable accelerated plate. These solutions, presented under integral and series forms in terms of the generalized Mittag-Leffler function, are presented as the sum of two terms. The first term, represent the velocity field corresponding to a Newtonian fluid, and the se

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Publication Date
Thu Dec 30 2021
Journal Name
Iraqi Journal Of Science
The Classical Continuous Mixed Optimal Control of Couple Nonlinear Parabolic Partial Differential Equations with State Constraints

In this work, the classical continuous mixed optimal control vector (CCMOPCV) problem of couple nonlinear partial differential equations of parabolic (CNLPPDEs) type with state constraints (STCO) is studied. The existence and uniqueness theorem (EXUNTh) of the state vector solution (SVES) of the CNLPPDEs for a given CCMCV is demonstrated via the method of Galerkin (MGA). The EXUNTh of the CCMOPCV ruled with the CNLPPDEs is proved. The Frechet derivative (FÉDE) is obtained. Finally, both the necessary and the sufficient theorem conditions for optimality (NOPC and SOPC) of the CCMOPCV with state constraints (STCOs) are proved through using the Kuhn-Tucker-Lagrange (KUTULA) multipliers theorem (KUTULATH).

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Publication Date
Thu Sep 30 2021
Journal Name
Iraqi Journal Of Science
The Continuous Classical Boundary Optimal Control of Triple Nonlinear Elliptic Partial Differential Equations with State Constraints

    Our aim in this work is to study the classical continuous boundary control vector  problem for triple nonlinear partial differential equations of elliptic type involving a Neumann boundary control. At first, we prove that the triple nonlinear partial differential equations of elliptic type with a given classical continuous boundary control vector have a unique "state" solution vector,  by using the Minty-Browder Theorem. In addition, we prove the existence of a classical continuous boundary optimal control vector ruled by the triple nonlinear partial differential equations of elliptic type with equality and inequality constraints. We study the existence of the unique solution for the triple adjoint equations

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Publication Date
Sun Jul 02 2023
Journal Name
Iraqi Journal Of Science
Peristaltic Transport of a Viscoelastic Fluid with Fractional Maxwell Model in an Inclined Channel

This paper is devoted to the study of the peristaltic transport of viscoelastic non-Newtonian fluids with fractional Maxwell model in an inclined channel. Approximate analytical solutions have been constructed using Adomain decomposition method under the assumption of long wave boundary layer type approximation and low Reynolds number. The effect of each of relaxation time, fractional parameters, Reynolds number, Froude number, inclination of channel and amplitude on the pressure difference, friction force and stream function along one wavelength are received and analyzed.

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