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On the natural solution of an impulsive fractional differential equation of order $q\in \left(1,2\right)$. (English) Zbl 1248.35226
Summary: This paper is motivated from some recent papers treating the impulsive Cauchy problems for some differential equations with fractional order $q\in \left(1,2\right)$. 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.
##### MSC:
 35R12 Impulsive partial differential equations 35R11 Fractional partial differential equations 37C25 Fixed points, periodic points, fixed-point index theory
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