Nonlocal Impulsive Fractional Integral Boundary Value Problem for (?k,?k)-Hilfer Fractional Integro-Differential Equations

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