Stability of solutions to impulsive Caputo fractional differential equations

Abstract

Stability of the solutions to a nonlinear impulsive Caputo fractional differential equation is studied using Lyapunov like functions. The derivative of piecewise continuous Lyapunov functions among the nonlinear impulsive Caputo differential equation of fractional order is defined. This definition is a natural generalization of the Caputo fractional Dini derivative of a function. Several sufficient conditions for stability, uniform stability and asymptotic uniform stability of the solution are established. Some examples are given to illustrate the results.

Keywords

• Stability
• Caputo derivative
• Lyapunov functions
• impulses
• fractional differential equations