Abstract
A method is used to solve the Fredholm–Volterra integral equation of the first kind in the space
L
2(Ω)×C(0,T)
,
Ω=
(x,y)∈
Ω:
x
2+y
2
⩽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 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.