Fredholm–Volterra integral equation and generalized potential kernel

摘要

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)∈Ω:x2+y2⩽a,z=0andT<∞.The kernel of the Fredholm integral term considered in the generalized potential form belongs to the class C([Ω]×[Ω]), while the kernel of the Volterra integral term is a positive and continuous function which belongs to the class C[0,T). 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.