Fredholm-Volterra integral equation with potential kernel

Abstract

A method is used to solve the Fredholm-Volterra integral equation of the first kind in the space $L_2(\Omega) x C(0, T), \Omega =[(x,y)\in\Omega:\sqrt{x^2+y^2}\leq a,z=0]$ and $T<\infty$. The kernel of the Fredholm integral term is considered in the generalized potential form belongs to the class C $([\Omega] x [\Omega])$, 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.