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Abstract
Significant advancements have been made in the theory of integral equations. The division of initial value problems into Volterra Integral Equations and boundary value problems into Fredholm Integral Equations is an essential framework. Simplifying these equations requires focusing on the kernel and considering various cases of it. In this study, only the Homogeneous Fredholm Integral Equations of the second kind are discussed. The article begins with an exploration of key concepts such as eigenvalues, eigenfunctions, and the related theorems, providing a comprehensive explanation of their roles.
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References
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References
D. C. Sharma, D. C. Goyal , PHI publishing. 2017; 29-36.
Dr. M. D. raising HANIA Integral equations and boundary value problem, new-Delhi. S.CHAND publisher. (2018); 31-40.
F.G TRICOMI integral equation, DOVER publishing (1955); 49-76.
Bochar, M. An introduction to the study of Antegral Equation. Cambridge Tracts;115-117.
Davis, H.T. the Present Status of integral Equation. Indiana University Studies;73-74.
Davis, H.T. The theory of Voltera Integral Equation of the Second kind , Indiana University;103-106
Heywood, H.B., and Frechet, Fredholm integral Equation and it’s application to physic, 3rd Edition , paris,1923; 89-93.
Carleman, T.sur integral Equation singularities Symetrique University, Arsskrift;3-10.