On the natural solution of an impulsive fractional differential equation of order q ∈ (1, 2)

This paper is motivated from some recent papers treating the impulsive Cauchy problems for some differential equations with fractional order q ∈ (1, 2). A better definition of solution for impulsive fractional differential equation is given. We build up an effective way to find natural solution for such problems. Then sufficient conditions for existence of the solutions are established by applying fixed point methods. Four examples are given to illustrate the results.

► A better definition of solution for impulsive fractional differential equation is given. ► An effective way to find natural solution for impulsive fractional Cauchy problem is built upon. ► Many new existence results of natural solutions are established again.