Existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative fractional differential equation

Abstract

In this work, we study the existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative Caputo fractional differential equation by first inverting it as an integral equation. Then we construct an appropriate mapping and employ the Schauder fixed point theorem to prove our new results. At the end we give an example to illustrate our obtained results.

Keywords

• iterative fractional differential equations
• fixed point theorem
• existence
• uniqueness
• continuous dependence
• ulam stability