Fredholm-Volterra Integral Equation with Potential Kernel

M. A. Abdou; A. A. El-Bary

doi:10.3390/mca6020113

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Article

1 August 2001

Fredholm-Volterra Integral Equation with Potential Kernel

and

Department of Mathematics, Faculty of Education, Alexandria University, Egypt

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.

Math. Comput. Appl.2001, 6(2), 113-122;https://doi.org/10.3390/mca6020113

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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

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