Abstract:
In this work, the existence of a unique solution of mixed integral equation (MIE) of the second kind is considered, in the space , where in the domain of integration and is the time. The kernel of position is considered in a generalized potential form. A numerical method is used to obtain system of Fredholm integral equations (SFIEs). The existence of a unique solution of this system can be proved. Finally, many special cases are considered and established from the work and some numerical results are considered.

Keywords: Fredholm- Volterra integral equation (F-VIE), generalized potential kernel, degenerate method, linear algebraic system. MSC: 45 B05, 45G 10, 65R