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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on mdpi.com as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2001, 6(2), 113-122; https://doi.org/10.3390/mca6020113

Fredholm-Volterra Integral Equation with Potential Kernel

1
Department of Mathematics, Faculty of Education, Alexandria University, Egypt
2
Department of Basic and applied Sciences, P.oBox 1029 Alexandria, Arab Academy for Science and Technology and Maritime Transport, Egypt
*
Author to whom correspondence should be addressed.
Published: 1 August 2001
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Abstract

A method is used to solve the Fredholm-Volterra integral equation of the first kind in the space L2(Ω) × C(O, T), Ω = {(x, y) \(\in\) Ω : \(\sqrt{{x^2}+{y^2}}\) ≤ a, z = 0} and T < ∞. The kernel of the Fredholm integral term is considered in the generalized potential form belongs to the class C ([Ω] × [Ω]), while the kernel of Volterra integral term is a positive and continuous function belongs to the class C[0,T). Also in this work the solution of Fredholm integral equation of the second and first kind with a potential kernel is discussed. Many interesting cases are derived and established from the wok.
Keywords: Fredholm-Volterra integral equations; generalized potential kernel; logarithmic kernel; Carleman kernel; Jacobi polynomials Fredholm-Volterra integral equations; generalized potential kernel; logarithmic kernel; Carleman kernel; Jacobi polynomials
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Abdou, M.A.; El-Bary, A.A. Fredholm-Volterra Integral Equation with Potential Kernel. Math. Comput. Appl. 2001, 6, 113-122.

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