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

100%
Zhang X., Agarwal P., Liu Z., Peng H.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
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.
3
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System of fractional differential equations with Erdélyi-Kober fractional integral conditions

75%
Thongsalee N., Laoprasittichok S., Ntouyas S. K., Tariboon J.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
In this paper we study existence and uniqueness of solutions for a system consisting from fractional differential equations of Riemann-Liouville type subject to nonlocal Erdélyi-Kober fractional integral conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. Examples illustrating our results are also presented.
4
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Extended Riemann-Liouville type fractional derivative operator with applications

63%
Agarwal P., Nieto J. J., Luo M.-J.
Open Mathematics
|
2017
|
tom 15
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nr 1
1667-1681
EN
The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox’s H-function are also presented.
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