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Please cite this article as: J. Wang, Y. Zhang, On the concept and existence of solutions for fractional impulsive systems with Hadamard derivatives, Appl. Math. Lett. (2014), http://dx.Abstract In this paper, a class of nonlinear fractional order differential impulsive systems with Hadamard derivative is discussed. Firstly, a reasonable concept on the solutions of fractional impulsive Cauchy problems with Hadamard derivative and the corresponding fractional integral equations are established. Secondly, two fundamental existence results are presented by using standard fixed point methods. Finally, two examples are given to illustrate our theoretical results.

A one-step method which involves exfoliating graphite materials (GIMs) off into graphene materials (GEMs) in aqueous suspension of CL-20 and forming CL-20/graphene materials (CL-20/GEMs) composites by using ball milling is presented. The conversion of mixtures to composite form was monitored by scanning electron microscopy (SEM) and powder X-ray diffraction (XRD). The impact sensitivities of CL-20/GEM composites were contrastively investigated. It turned out that the energetic nanoscale composites based on CL-20 and GEMs comprising few layers were accomplished. The loading capacity of graphene (reduced graphene oxide, rGO) is significantly less than that of graphene oxide (GO) in CL-20/GEM composites. The formation mechanism was proposed. Via this approach, energetic nanoscale composites based on CL-20 and GO comprised few layers were accomplished. The resulted CL-20/GEM composites displayed spherical structure with nanoscale, ε-form, equal thermal stabilities, and lower sensitivities.Electronic supplementary materialThe online version of this article (10.1186/s11671-017-2416-y) contains supplementary material, which is available to authorized users.

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