Existence and uniqueness for a class of iterative fractional differential equations

Abstract

The presence of a self-mapping increases the difficulty in proving the existence and uniqueness of solutions for general iterative fractional differential equations. In this article, we provide conditions for the existence and uniqueness of solutions for the initial value problem. We also determine the Burton stability of such equations. The arbitrary order case is taken in the sense of Riemann-Liouville fractional operators.