The existence and uniqueness of solution for linear system of mixed Volterra-Fredholm integral equations in Banach space

Hasan, Pakhshan Mohammed Ameen; Sulaiman, Nejmaddin A.; Soleymani, Fazlollah; Akgül, Ali

doi:10.3934/math.2020014

Cited by 9 publications

(6 citation statements)

References 8 publications

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“…There are many numerical integration methods to evaluate composite integrals; in this paper, we use two numerical quadrature methods, Simpsons 3/8 method, and Boole's method [15][16][17][18][19][20][21][22][23].…”

Section: Solutions Of the Problemmentioning

confidence: 99%

Numerical solution for time period of simple pendulum with large angle

et al. 2020

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In this study, the numerical solution of the ordinary kind of differential equation for a simple pendulum with large-angle of oscillation was introduced to obtain the time period. The analytical solution is obtained in terms of elliptic functions, and numerical solution of the problem was achieved by using two numerical quadrature methods, namely, Simpson?s 3/8 and Boole?s method. The period of a simple pendulum with large angle is presented; a comparison has been carried out between the analytical solution and the numerical integration results. In the case of error analysis, absolute and relative errors of the problem have been presented. A numerical algorithm has been developed by Matlab software 2013R and used for analyzing the result. It is established that the results of the comparison guaranty the ability and the accuracy of the present method.

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Section: Solutions Of the Problemmentioning

confidence: 99%

Numerical solution for time period of simple pendulum with large angle

et al. 2020

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“…Mirzaee and Hoseini [6] discussed the solution of The linear mixed Volterra-Fredholm integral equation using Fibonacci collocation method, while the numerical solution via modification of the hat function was presented in [7]. Hasan and Sulaiman [8] studied the existence and uniqueness results for the linear mixed Volterra-Fredholm integral equation is given by…”

Section: Introductionmentioning

confidence: 99%

Boundary Value Problem of Nonlinear Fractional Differential Equations of Mixed Volterra-Fredohlm Integral Equations in Banach Space

Taier,

Wu,

Iqbal

2024

AJAM

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This paper is dedicated to study the existence and uniqueness of solutions for a boundary value problem of nonlinear fractional differential equations of mixed Volterra-Fredohlm integral equations in Banach space, the recent researches considered the study of differential equations of mixed Volterra-Fredholm integral equations with classical order and the study of existence and uniqueness of solutions using approched numerical methodes, the objective of this paper is the study of the existence and uniqueness of fractional order of differential equations with mixed Volterra-Fredholm integral equations using fixed point theory. This work have two important results, the first result was the discussion of the existence of solutions using the Krasnoselskii fixed point theorem after transforming the problem into integral equation firstly then into operator problem suitable for the fixed point theory. The second result will be the existence and uniqueness of solution, this result was obtained by the use of Banach fixed point theorem after the same transformation used in the first one. This work give as conclusion that the boundary value problem of nonlinear fractional differential equations of mixed Volterra-Fredholm integral equation has a unique solution in Banach space. Finally, this work was ended with an example to illustrate the results obtained.

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“…Rabiei et al (2019) they considered a third order General Linear Method for finding the numerical solution of Volterra integrodifferential equation . Hasan and Suleiman (2018) by applying Linear Programming problem demonstrated the numerical solution of mixed Voltera-Fredholm integral equations. Hassan et al (2017) applied Aitken method for solving Volterra-Fredholm integral equations of the second kind with Homotopy perturbation technique.…”

Section: Introductionmentioning

confidence: 99%

SEE Transform Technique for Solving System of Linear Volterra Integro-Differential Equations of the Second Kind

Rustam

Sulaiman

2023

Polytechnic j.

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There are many integral transforms that are widely used to solve numerous real-life, science, and engineering problems. In this article, we present SEE transform for determining the solution of the system of linear Volterra integro-differential equations of the second kind. Some applications have been given and solved by using the SEE transform for illustrating the applicability of the SEE transform. Results of the applications assert that the SEE transform is very effective for obtaining the exact solution of this equation.

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The existence and uniqueness of solution for linear system of mixed Volterra-Fredholm integral equations in Banach space

Cited by 9 publications

References 8 publications

Numerical solution for time period of simple pendulum with large angle

Numerical solution for time period of simple pendulum with large angle

Boundary Value Problem of Nonlinear Fractional Differential Equations of Mixed Volterra-Fredohlm Integral Equations in Banach Space

SEE Transform Technique for Solving System of Linear Volterra Integro-Differential Equations of the Second Kind

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