Existence and Stability Results for Caputo-Type Sequential Fractional Differential Equations with New Kind of Boundary Conditions

In this paper, we present the existence and the stability results for a nonlinear coupled system of sequential fractional differential equations supplemented with a new kind of coupled boundary conditions. Existence and uniqueness results are established by using Schaefer’s fixed point theorem and Banach’s contraction mapping principle. We examine the stability of the solutions involved in the Hyers–Ulam type. A few examples are presented to illustrate the main results.