Existence Results and Ulam–Hyers Stability for a Fully Coupled System of Nonlinear Sequential Hilfer Fractional Differential Equations and Integro-Multistrip-Multipoint Boundary Conditions

In this paper, we investigate the existence of solutions for a new coupled system of sequential Hilfer fractional differential equations equipped with coupled integro-multistrip-multipoint boundary conditions. We make use of the incomplete gamma function to evaluate the integrals involved in the solution of the problem. The uniqueness result for the given problem is obtained by the Banach contraction mapping principle, while the existence results are established with the aid of Krasnosel’skiĭ’s fixed point theorem and Leray–Schauder nonlinear alternative under different assumptions. We also discuss the Ulam–Hyers stability for the problem at hand. Numerical examples are constructed for the illustration of the abstract results.