International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 6, Pages 321-330

Fredholm-Volterra integral equation with potential kernel

M. A. Abdou1 and A. A. El-Bary2

1Department of Mathematics, Faculty of Education, Alexandria University, Egypt
2Department of Basic and Applied Sciences, P.O. Box 1029 Alexandria, Arab Academy for Science and Technology and Maritime Transport, Egypt

Received 9 October 2000

Copyright © 2001 M. A. Abdou and A. A. El-Bary. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A method is used to solve the Fredholm-Volterra integral equation of the first kind in the space L2(Ω)×C(0,T), Ω={(x,y):x2+y2a}, z=0, and T<. The kernel of the Fredholm integral term 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 that 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 in the paper.