Nonlinear impulsive problems for uncertain fractional differential equations

Abstract

This paper deals with the impulsive problem for uncertain fractional dynamical system. Firstly, the concept of uncertain fractional impulsive problem involving the Caputo derivative is introduced and the analytic solutions to several linear uncertain fractional impulsive problems are derived with the help of the Mittag-Leffler functions. Then the existence and uniqueness theorems are developed via the Kuratowski measure of noncompactness and fixed point theorems, respectively. Finally, an illustrative example is provided to explain our main results.