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On the concept of general solution for impulsive differential equations of fractional-orderq∈ (2,3)

100%
Zhang X., Shu T., Liu Z., Ding W., Peng H., He J.
Open Mathematics
|
2016
|
tom 14
|
nr 1
452-473
EN
In this paper, we find the formula of general solution for a generalized impulsive differential equations of fractional-order q ∈ (2, 3).
2
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The general solution of impulsive systems with Riemann-Liouville fractional derivatives

100%
Zhang X., Ding W., Peng H., Liu Z., Shu T.
Open Mathematics
|
2016
|
tom 14
|
nr 1
1125-1137
EN
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.
3
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Oscillation of impulsive conformable fractional differential equations

76%
Tariboon J., Ntouyas S. K.
Open Mathematics
|
2016
|
tom 14
|
nr 1
497-508
EN
In this paper, we investigate oscillation results for the solutions of impulsive conformable fractional differential equations of the form tkDαpttkDαxt+rtxt+qtxt=0,t≥t0,t≠tk,xtk+=akx(tk−),tkDαxtk+=bktk−1Dαx(tk−),k=1,2,…. $$\left\{ \begin{array}{l} {t_k}{D^\alpha }\left( {p\left( t \right)\left[ {{t_k}{D^\alpha }x\left( t \right) + r\left( t \right)x\left( t \right)} \right]} \right) + q\left( t \right)x\left( t \right) = 0,\quad t \ge {t_0},\;t \ne {t_k},\\ x\left( {t_k^ + } \right) = {a_k}x(t_k^ - ),\quad {t_k}{D^\alpha }x\left( {t_k^ + } \right) = {b_{k\;{t_{k - 1}}}}{D^\alpha }x(t_k^ - ),\quad \;k = 1,2, \ldots. \end{array} \right.$$ Some new oscillation results are obtained by using the equivalence transformation and the associated Riccati techniques.
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