Caputo Proportional Fractional Differential Equation with Multi-point Boundary Condition

This is the authors' abstract. We don't add key points for this paper.

In this article, inspired by the proportional fractional derivative, we investigate the uniqueness of the solutions for generalized Caputo proportional differential equations with multi-point boundary conditions. We convert the formulated problem into an equivalent integral equation with the support of Green's function. The results we obtain generalize many other existing results compared with the Caputo type classical fractional differential equations.