Existence and stability for a boundary value problem of Ambartsumian equation with -Hilfer generalized proportional fractional derivative

In this paper, we prove the existence and uniqueness of solution for the mixed boundary value problem of Ambartsumian equation using -Hilfer generalized proportional fractional derivative(PFD). The main principles applied to investigate our results are based on the standard fixed point theorems. We dewell in detail on some results concerning the Hyers-Ulam type stability. We verify our result with an illustrative example