## A survey and new investigation on $$(n,n-k)$$-type boundary value problems for higher order impulsive fractional differential equations.(English)Zbl 1403.34002

In this paper, the author firstly takes a survey for some existing results on boundary value problems of higher order ordinary differential equations. Then, the author makes a review for some literature on the solvability of boundary value problems for impulsive fractional differential equations. Thirdly, the author considers existence results of solutions for three classes of $$(n,n-p)$$-type boundary value problems of impulsive higher order fractional differential equations by using some standard fixed point theorems in Banach space. Some examples are presented to illustrate the efficiency of the obtained results. Finally, the author gives some future research topics on impulsive fractional differential equations.

### MSC:

 34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations 34A08 Fractional ordinary differential equations 34A37 Ordinary differential equations with impulses 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B37 Boundary value problems with impulses for ordinary differential equations 47N20 Applications of operator theory to differential and integral equations
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