Particular integral equation

Question

Let $a,\sigma, n>0$ be some parameters and define the conditional probability density function $$ p(x,y):= \frac{1}{\sigma\sqrt{2\pi}}\exp\left(-\frac{(y-n-x)^2}{2\sigma^2}\right). $$ Is it possible to express the solution of the following integral equation using some known functions? $$ f_a(x,y) = p(x,y) + \int_0^af_a(x',y)p(x,x')\mathrm dx'. $$