Differential equations of arbitrary order under Caputo-Fabrizio derivative: some existence results and study of stability

Abstract

In this work, we consider the problem of the existence and uniqueness of solution, and also the simple existence of solution, for implicit differential equations of arbitrary order involving Caputo-Fabrizio derivative. The main tools for this study are contraction mapping principle and Schaefer's fixed point result. We also study the stability of the equations in the sense of Ulam-Hyers and also from the perspective of Ulam-Hyers-Rassias.

Keywords

• fractional differential equations
• caputo-fabrizio fractional derivative
• fixed point theorems
• contractive maps
• functional equations
• gronwall inequality
• ulam-hyers stability
• ulam-hyers-rassias stability