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 L2(Ω)×C(0,T), Ω={(x,y):x2+y2≤a}, 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.