Mixed-order impulsive ordinary and fractional differential equations with initial conditions

Abstract

Abstract In this paper, using the idea of separated intervals in non-instantaneous impulsive equations, we initiate the study of initial value problems for mixed-order ordinary and fractional differential equations with instantaneous impulsive effects. Existence and uniqueness results are established via standard fixed point theorems. Examples illustrating the main results are also presented.

Keywords

• Impulsive differential equations
• Fractional impulsive differential equations
• Instantaneous impulses
• Non-instantaneous impulses