New results on a coupled system for second-order pantograph equations with ABC fractional derivatives

Abstract

The aim of this paper is to demonstrate a coupled system of second-order fractional pantograph differential equations with coupled four-point boundary conditions. The proposed system involves Atangana-Baleanu-Caputo (ABC) fractional order derivatives. We prove the solution formula for the corresponding linear version of the given system and then convert the system to a fixed point system. The existence and uniqueness results are obtained by making use of nonlinear alternatives of Leray-Schauder fixed point theorem, and Banach's contraction mapping. In addition, the guarantee of solutions for the system at hand is shown by the stability of Ulam-Hyers. Pertinent examples are provided to illustrate the theoretical results.

Keywords

• pantograph system
• abc fractional derivative
• existence
• fixed point theorem