Problem on piecewise Caputo-Fabrizio fractional delay differential equation under anti-periodic boundary conditions

Abstract

This manuscript considers a class of piecewise differential equations (DEs) modeled with the Caputo-Fabrizio differential operator. The proposed problem involves a proportional delay term and is equipped with anti-periodic boundary conditions. The piecewise derivative can be applied to model many complex nature real-world problems that show a multi-step behavior. The existence theory and Hyer-Ulam (HU) stability results are studied for the proposed problem via fixed point techniques such as Banach contraction theorem, Schauder’s fixed point theorem and Arzelá Ascoli theorem. A numerical problem is presented as an example to see the validity and effectiveness of the applied concept.