Fractional differential equations with anti-periodic fractional integral boundary conditions via the generalized proportional fractional derivatives

Abstract

This paper is dedicated to studying the existence and uniqueness of solutions to a system of fractional differential equations with anti-periodic fractional integral boundary conditions in the frame of the generalized pro- portional fractional derivatives of Riemann-Liouville type. With the aid of the Schaefer fixed point theorem and the Banach fixed point theorem, the main results are established. An example is proposed to illustrate the applicability of the theoretical results.