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Copyright of Kirkuk Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The main objective of this paper is to introduce interval two-point fuzzy boundary value problems, in which the fuzziness course when the coefficients of the governing ordinary differential equation and/or the boundary conditions include fuzzy numbers of either triangular or trapezoidal types. Such equations will be solved by introducing the concept of α – level sets, α  [0,1] to treat the fuzzy ordinary differential equation into two nonfuzzy ordinary differential equations, which correspond to the lower and upper solutions of the interval fuzzy solutions. The well-known variational iteration method has been used to solve two-point fuzzy boundary value problems and linear equations have been examined. [ABSTRACT FROM AUTHOR]

Copyright of Journal of University of Anbar for Pure Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of University of Anbar for Pure Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Ordinary differential equations that includes stochastic processes in their vector fields are called random ordinary differential equations, that are considered through this work as a Weiner process or also called Brownian motion. In this paper, fuzzy random ordinary differential equations are considered, in which the fuzziness appears in the initial conditions in terms of triangular fuzzy numbers. Such equations are crucial in the theory of random dynamical systems and/or modern control theory and therefore the existence of a unique solution of such equations is of great importance. The statement and the proof of the existence and uniqueness theorem of fuzzy random ordinary differential equations is the main objective of this paper, which is proved using Banach contraction mapping theorem. [ABSTRACT FROM AUTHOR]

Copyright of Iraqi Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of the College Of Basic Education is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, the continuous Boubaker scaling functions were constructed with the presentation on the interval [0,1], which obtained depending on Boubaker polynomials. In this study the Boubaker scaling polynomial has been applied for solving the nth order integro–differential equations (IDE’s).The collocation method with the aid of Boubaker scaling functions together were utilized to transform the higher order integro–differential equations into a linear system algebraic equations. Some numerical examples were added to show the simplicity and accuracy of the proposed technique. The results have been compared with the exact solution using MATLAB and illustrated by graphs. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Education & Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Education & Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of University of Anbar for Pure Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Iraqi Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Iraqi Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Iraqi Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this research paper, the backstepping method (BSM) will be proposed for stabilizing and solving system of 2×2 Riccati matrix ordinary differential equations. Such equations have many difficulties in the studying their solutions and stability. The basic idea behind of this approach is to use the BSM as a transformation method for transforming the original system into an equivalent one which is stabilizable and solvable based on constructing the Lyapunov function. [ABSTRACT FROM AUTHOR]

In this paper, some conditions to guarantee the existence of bounded solution to the second order multi delayed arguments differential equation are given. The Krasnoselskii theorem used to the Lebesgue’s dominated convergence and fixed point to obtain some new sufficient conditions for existence of solutions. Some important lemmas are established that are useful to prove the main results for oscillatory property. We also submitted some sufficient conditions to ensure the oscillation criteria of bounded solutions to the same equation. [ABSTRACT FROM AUTHOR]

In this paper, we apply double sumudu transform coupled with a numerical method "a new iterative method" to solve some of fractional partial differential equations which cannot be solved by applying double Sumudu transform only. Several examples illustrate with plotting their solutions are given. [ABSTRACT FROM AUTHOR]

This paper presents an approximate solution of ordinary boundary value problems using the variational iteration method. The fractional derivatives are described in the Caputo sense, because it allows traditional initial and boundary conditions to be included in the formulation of the problem. The solutions of proposed fractional equations are calculated in the form of convergent series with easily computable components. Also, we construct the variational iteration formula and its convergence to the exact solution for solving system of fractional order differential equations. Some examples are solved as an illustration to the method, in order to show the accuracy of the method and comparison with results the exact solution for the given test problems, which are given for comparison purpose. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Qadisiyah Computer Science & Mathematics is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, the function of the pond's seepage problem is derived using versional approach as especial case of generalized dam problem. In this problem the two dimensional cross section will produce problem with two free surfers which are evaluated as a part of the problem using simulating computer program. [ABSTRACT FROM AUTHOR]

Copyright of Iraqi Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Iraqi Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

this paper dedicated to the construction of solution of a three time scale periodic singular perturbed nonlinear quadratic optimal control problem by using the direct method. The algorithm of the method is the direct substitution of the postulated asymptotic expansion of the solution of the problem and then by the conditions of the problem we constructed of a series of problem and find terms of the asymptotic. We find the solution by using the Hamilton's function and maximum principle. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Qadisiyah Computer Science & Mathematics is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper we present a computational method for solving delay differential equations of fractional order by employing the Laplace Adomian decomposition method. This method is combined from the Laplace transforms and the Adomian decomposition method taking into account the Caputo derivative as a motivation to describe the fractional derivative. The method is a modification of the Adomian decomposition method and is tested on two examples in order to illustrate the pertinent feature of this method the results shows that the proposed method is an effective and powerful tool for solving delay differential equations of fractional order. A comparison with the exact solution and with the existing methods such as Adomian decomposition method and homotopy analysis method is made. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a reliable iterative method for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method. Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibits that this technique was compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations. [ABSTRACT FROM AUTHOR]

This paper presents a new numerical method for the solution of ordinary differential equations (ODE). The linear second-order equations considered herein are solved using operational matrices of Wang-Ball Polynomials. By the improvement of the operational matrix, the singularity of the ODE is removed, hence ensuring that a solution is obtained. In order to show the employability of the method, several problems were considered. The results indicate that the method is suitable to obtain accurate solutions. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Education & Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, the oscillatory and nonoscillatory qualities for every solution of fourth-order neutral delay equation are discussed. Some conditions are established to ensure that all solutions are either oscillatory or approach to zero asદ →∞. Two examples are provided to demonstrate the obtained findings. [ABSTRACT FROM AUTHOR]

Copyright of Iraqi Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Iraqi Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, a mathematical model consisting of the food chain model with disease in intermediate predator is proposed and discussed. The food chain model consists of four types: prey, intermediate predator, infected intermediate predator, and top predator. We studied the solutions for the original model and positive and bounded solutions in the sub models. Also found equilibrium points with sufficient and necessary conditions. By using Jacobian matrix and Lyapunov function to provide local and global stability. Can use the harvesting to control the disease and it can be used as tool to prevent disease transformation into an epidemic. Finally, some results were illustrated in numerical simulations. [ABSTRACT FROM AUTHOR]

Copyright of Basrah Journal of Science / Magallat Al-Barat Li-L-ulum is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Basrah Journal of Science / Magallat Al-Barat Li-L-ulum is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Qadisiyah Computer Science & Mathematics is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Basrah Journal of Science / Magallat Al-Barat Li-L-ulum is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Qadisiyah Computer Science & Mathematics is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Education & Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Qadisiyah Computer Science & Mathematics is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, the existence of the global solution and its uniqueness is studied for the Second Order Nonlinear Integro-Differential Fractional Equations with boundary conditions by utilizing the Picard approximation method which is given by Sturble, 1962. Furthermore, several given results by Butris, 2010 have been extended [ABSTRACT FROM AUTHOR]

Copyright of Al-Mustansiriyah Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper we introduce presents a numerical approach, based on radial basis function networks (RBFNS), for the approximation of a function and its derivatives (scattered data interpolation), The proposed approach here is called the indirect radial basis function network (IRBFN) to solve second and fourth order differential equations the procedure can start with the second derivative. First, the second order derivative is approximated by a RBFN, then the first order derivative is obtained by integration. Finally the original function is similarly obtained, i.e. by integrating the first derivative function. This second method is here referred to as the second indirect method or IRBFN2 likewise fourth -grade derivative IRBFN4. [ABSTRACT FROM AUTHOR]

The idea of the paper is to consolidate Mahgoub transform and variational iteration method (MTVIM) to solve fractional delay differential equations (FDDEs). The fractional derivative was in Caputo sense. The convergences of approximate solutions to exact solution were quick. The MTVIM is characterized by ease of application in various problems and is capable of simplifying the size of computational operations. Several non-linear (FDDEs) were analytically solved as illustrative examples and the results were compared numerically. The results for accentuating the efficiency, performance, and activity of suggested method were shown by comparisons with Adomian Decomposition Method (ADM), Laplace Adomian Decomposition Method (LADM), Modified Adomian Decomposition Method (MADM) and Homotopy Analysis Method (HAM). [ABSTRACT FROM AUTHOR]

This paper deals with finding an approximate solution to the index-2 time-varying linear differential algebraic control system based on the theory of variational formulation. The solution of index-2 time-varying differential algebraic equations (DAEs) is the critical point of the equivalent variational formulation. In addition, the variational problem is transformed from the indirect into direct method by using a generalized Ritz bases approach. The approximate solution is found by solving an explicit linear algebraic equation, which makes the proposed technique reliable and efficient for many physical problems. From the numerical results, it can be implied that very good efficiency, accuracy, and simplicity of the present approach are obtained. [ABSTRACT FROM AUTHOR]

In this paper, two trigonometrically methods were established based on classical Runge-Kutta methods of the fourth and fifth-order respectively. The new methods will be applied for the numerical integration of oscillatory problems and have high effectiveness as the results demonstrate. Numerical results show the robustness and competence of the new methods compared to the well-known Runge-Kutta methods in the scientific literature. [ABSTRACT FROM AUTHOR]

In this paper, we use the cubic B-splines method to solve the singular perturbed delay partial differential equations where the propagation term is multiplied by a small perturbation coefficient. In general, solutions to this type of problem have a boundary layer. The accuracy of the method was tested with two numerical examples and the results were compared with exact solutions and other methods. [ABSTRACT FROM AUTHOR]

This paper presents a numerical scheme for solving nonlinear time-fractional differential equations in the sense of Caputo. This method relies on the Laplace transform together with the modified Adomian method (LMADM), compared with the Laplace transform combined with the standard Adomian Method (LADM). Furthermore, for the comparison purpose, we applied LMADM and LADM for solving nonlinear time-fractional differential equations to identify the differences and similarities. Finally, we provided two examples regarding the nonlinear timefractional differential equations, which showed that the convergence of the current scheme results in high accuracy and small frequency to solve this type of equations. [ABSTRACT FROM AUTHOR]

Copyright of Basrah Journal of Science / Magallat Al-Barat Li-L-ulum is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of College of Education is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of University of Anbar for Pure Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)