Coupled systems of $\psi$-Hilfer generalized proportional fractional nonlocal mixed boundary value problems

In this paper, we investigate a coupled system of Hilfer-type nonlinear proportional fractional differential equations supplemented with mixed multi-point and integro-multi-point boundary conditions. We used standard methods from functional analysis and especially fixed point theory. Two existence results are established using the Leray-Schauder's alternative and the Krasnosel'skii's fixed point theorem, while the existence of a unique solution is achieved via the Banach's contraction mapping principle. Finally, numerical examples are constructed to illustrate the main theoretical results. Our results are novel, wider in scope, produce a variety of new results as special cases and contribute to the existing literature on nonlocal systems of nonlinear $\psi$-Hilfer generalized fractional proportional differential equations.