Fractional variable order differential equations with impulses: A study on the stability and existence properties

Abstract

In this paper, for the first time, we study the existence and uniqueness of solutions of a Caputo variable-order initial value problem (IVP) in the impulsive settings. Our existence results are proved by using two fixed point theorems. The Ulam-Hyers stability of solutions is established for the variable order impulsive initial value problem. Finally, we provide an example to show the correctness of the results.

Keywords

• impulsive condition
• differential equations
• fractional variable order
• ulam-hyers stability
• existence of solutions
• fixed point theorem