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The main theme of this thesis could be divided into three objectives : The first is to define and classify integral equations with one and multiple delay, including Fredholm, Volterra and integro-differential equations (Retarded, Neutral and Mixed types). While the second and popular objective of this work is to study the inverse problems related to delay integral equations by using non-classical variational formulation method. Some examples are given for each of the discussed type of delay integral equations. Also, a study to the direct and inverse problems related to integral equations with multiple delay, also considered as a third objective. Several examples are given for each type of these equations. Finally, the suggested approach

An approximate solution of the liner system of ntegral cquations fot both fredholm(SFIEs)and Volterra(SIES)types has been derived using taylor series expansion.The solusion is essentailly

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تتمتع لبنان بمقومات مهمة في مجال القوة الناعمة، جعلته يمتلك تأثيرًا ثقافيًا وإعلاميًا يتجاوز مساحته الجغرافية وحجمه السكاني. وتتمثل أبعاد القوة الناعمة اللبنانية في عدة جوانب رئيسية، أبرزها البعد الثقافي الذي يظهر من خلال التنوع الثقافي والانفتاح الفكري، فضلًا عن الأدب والفنون والموسيقى. كما يبرز البعد الإعلامي عبر الحضور المؤثر للإعلام اللبناني في العالم العربي، خاصة في مجالات الصحافة والإنتاج التلفزيو

Intended for getting good estimates with more accurate results, we must choose the appropriate method of estimation. Most of the equations in classical methods are linear equations and finding analytical solutions to such equations is very difficult. Some estimators are inefficient because of problems in solving these equations. In this paper, we will estimate the survival function of censored data by using one of the most important artificial intelligence algorithms that is called the genetic algorithm to get optimal estimates for parameters Weibull distribution with two parameters. This leads to optimal estimates of the survival function. The genetic algorithm is employed in the method of moment, the least squares method and the weighted

This paper considers approximate solution of the hyperbolic one-dimensional wave equation with nonlocal mixed boundary conditions by improved methods based on the assumption that the solution is a double power series based on orthogonal polynomials, such as Bernstein, Legendre, and Chebyshev. The solution is ultimately compared with the original method that is based on standard polynomials by calculating the absolute error to verify the validity and accuracy of the performance.

     The primary objective of the current paper is to suggest and implement effective computational methods (DECMs) to calculate analytic and approximate solutions to the nonlocal one-dimensional parabolic equation which is utilized to model specific real-world applications. The powerful and elegant methods that are used orthogonal basis functions to describe the solution as a double power series have been developed, namely the Bernstein, Legendre, Chebyshev, Hermite, and Bernoulli polynomials. Hence, a specified partial differential equation is reduced to a system of linear algebraic equations that can be solved by using Mathematica®12. The techniques of effective computational methods (DECMs) have been applied to solve some s