Fredholm solutions of partial integral equations

Abstract

In this article, we have considered the following partial integral equation $\phi(x,y)=f(x,y)+\lambda_1 \int_a^b (K_1)(x,t).\phi(t,y) dt+\lambda_2 \int_a^b (K_2)(y,s)\phi(x,s)ds$ and, under some conditions, we proved that the partial integral equation is equivalent to the Second Type Fredhoim's Integral Equation.