Abstract
In this paper, we establish the existence and stability results for the (rho(k),phi(k))-Hilfer fractional integro-differential equations under instantaneous impulse with non-local multi-point fractional integral boundary conditions. We achieve the formulation of the solution to the (rho(k),phi(k))-Hilfer fractional differential equation with constant coefficients in term of the Mittag-Leffler kernel. The uniqueness result is proved by applying Banach's fixed point theory with the Mittag-Leffler properties, and the existence result is derived by using a fixed point theorem due to O'Regan. Furthermore, Ulam-Hyers stability and Ulam-Hyers-Rassias stability results are demonstrated via the non-linear functional analysis method. In addition, numerical examples are designed to demonstrate the application of the main results.