Fredholm-Volterra integral equation and generalized potential kernel

A method is used to solve the Fredholm–Volterra integral equation of the first kind in the space L2ðXÞ Cð0; T Þ, X 1⁄4 ðx; yÞ 2 X: ffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 þ y2 p n 6 a; z 1⁄4 0 o and T < 1: The kernel of the Fredholm integral term considered in the generalized potential form belongs to the class Cð1⁄2X 1⁄2X Þ, while the kernel of the Volterra integral term is a positive and continuous function which belongs to the class C1⁄20; T Þ. Also in this work the solution of the Fredholm integral equation of the first and second kind with a generalized potential kernel is discussed. Many interesting cases are derived and established from the work. 2002 Elsevier Science Inc. All rights reserved.