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The general solution for impulsive differential equations with Riemann-Liouville fractional-order q ∈ (1,2)

Xianmin Zhang;  Praveen Agarwal;  Zuohua Liu;  Hui Peng — 2015

Open Mathematics

In this paper we consider the generalized impulsive system with Riemann-Liouville fractional-order q ∈ (1,2) and obtained the error of the approximate solution for this impulsive system by analyzing of the limit case (as impulses approach zero), as well as find the formula for a general solution. Furthermore, an example is given to illustrate the importance of our results.

The general solution of impulsive systems with Riemann-Liouville fractional derivatives

Xianmin Zhang;  Wenbin Ding;  Hui Peng;  Zuohua Liu;  Tong Shu — 2016

Open Mathematics

In this paper, we study a kind of fractional differential system with impulsive effect and find the formula of general solution for the impulsive fractional-order system by analysis of the limit case (as impulse tends to zero). The obtained result shows that the deviation caused by impulses for fractional-order system is undetermined. An example is also provided to illustrate the result.

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